Class 11

Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions

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Tamilnadu Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions

Samacheer Kalvi 11th Chemistry Chapter 9 Solutions Textual Evaluation Solved

Samacheer Kalvi 11th Chemistry Solutions Multiple Choice Questions

Question 1.
The molality of a solution containing 1 .8g of glucose dissolved in 250g of water is …………
(a) 0.2 M
(b) 0.01 M
(c) 0.02 M
(d) 0.04 M
Answer:
(d) 0.04 M
Solution:
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-1

Question 2.
Which of the following concentration terms is/are independent of temperature?
(a) molality
(b) molarity
(c) mole fraction
(d) (a) and (c)
Answer:
(d) (a) and (c)
Solution:
Molality and mole fraction are independent of temperature.

Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions

Question 3.
Stomach acid, a dilute solution of HCI can be neutralised by reaction with Aluminium hydroxide
Al(OH)3 + 3HCl(aq) → AlCl3 + 3H2O
How many millilitres of 0.1 M Al(OH)3 solution are needed to neutralise 21 mL of 0.1 M HCl
(a) 14 mL
(b) 7 mL
(c) 21 mL
(d) none of these
Answer:
(b) 7 mL
Solution:
M1 x V1 = M2 x V2
∵ 0.1 M Al(OH)3 gives 3 x 0.1 = 0.3 M OH ions .
0.3 x V1 = 0.1 x 21
V1= \(\frac { 0.1 x 21 }{ 0.3 }\) = 7ml

Question 4.
The partial pressure of nitrogen in air is 0.76 atm and its Henry’s law constant is 7.6 x 104 atm at 300K. What is the mole fraction of nitrogen gas in the solution obtained when air is bubbled through water at 300K?
(a) 1 x 10-4
(b) 1 x 10-6
(c) 2 x 10-5
(d) 1 x 10-5
Answer:
(d) 1 x 10-5
Solution:
PN2 = 0.76atm
KH = 7.6 x 104
x = ?
PN2 = KH . x
0.76 = 7.6 x 104x x
x = \(\frac { 0.76 }{ 7.6\times { 10 }^{ 4 } }\) = 1 x 10-5

Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions

Question 5.
The Henry’s law constant for the solubility of Nitrogen gas in water at 350K is 8 x 104 atm. The mole fraction of nitrogen in air is 0.5. The number of moles of Nitrogen from air dissolved in 10 moles of water at 350K and 4 atm pressure is ………….
(a) 4 x 10-4
(b) 4 x 104
(c) 2 x 10-2
(d) 2.5 x 10-4
Answer:
(d) 2.5 x 10-4
Solution:
KH = 8 x 104
(xN2 )in air = 0.5
Total pressure = 4 atm
Partial pressure of nitrogen = Mole fraction Total pressure
= O.5 x 4 = 2
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-3

Question 6.
Which one of the following is incorrect for ideal solution?
(a) ∆Hmix = 0
(b) ∆Umix = o
(c) ∆P = PObserved – PCalculated by raoults law = 0
(d) ∆Gmix = 0
Answer:
(d) ∆Gmix = 0
Solution:
For an ideal solution, ∆Smix \(\neq\) 0; Hence ∆Gmix \(\neq\) 0
∴ Incorrect is ∆Gmix = 0

Question 7.
Which one of the following gases has the lowest value of Henry’s law constant?
(a) N2
(b) He
(c) CO2
(d) H2
Answer:
(c) CO2
Solution:
Carbon dioxide; most stable gas and has lowest value of Henry’s Law constant.

Question 8.
P1 and P2 are the vapour pressures of pure liquid components, 1 and 2 respectively of an ideal binary solution if x1 represents the mole fraction of component 1, the total pressure of the solution formed by 1 and 2 will be ………
(a) P1 + x1(P2 – P1)
(b) P2 – x1(P2 + P1)
(c) P1 – x2(P1 – P2)
(d) P1 + x2(P1 – P2)
Answer:
(c) P1 – x2(P1 – P2)
Solution:
Ptotal = P1 + P2
= P1 x1 + P2x2
= P1(1 – x2) + P2x2
= P1 – P1x2 + P2x2 = P1 – x2(P1 – P2)
[∵x1 + x2 = 1
x1 = 1 – x2]

Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions

Question 9.
Osomotic pressure (π) of a solution is given by the relation ……………
(a) π = nRT
(b) πV = nRT
(c) πRT = n
(d) none of these
Answer:
(b) πV = nRT
Solution:
n = CRT
n = \(\frac { n }{ V }\)
π V = nRT

Question 10.
Which one of the following binary liquid mixtures exhibits positive deviation from Raoults law?
(a) Acetone + chloroform
(b) Water + nitric acid
(c) HCI + water
(d) ethanol + water
Answer:
(d) ethanol + water

Question 11.
The Henry’s law constants for two gases A and B are x and y respectively. The ratio of mole fractions of A to B is 0.2. The ratio of mole fraction of B and A dissolved in water will be …………
(a) \(\frac { 2x }{ y }\)
(b) \(\frac { y }{ 0.2x }\)
(c) \(\frac { 0.2x }{ y }\)
(d) \(\frac { 5x }{ y }\)
Answer:
(d) \(\frac { 5x }{ y }\)
Solution:
Given,
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-4

Question 12.
At 100°C the vapour pressure of a solution containing 6.5g a solute in 100g water is 732mm. If Kb = 0.52, the boiling point of this solution will be …………..
(a) 102°C
(b) 100°C
(c) 101°C
(d) 100.52°C
Answer:
(c) 101°C
Solution:
\(\frac { ΔP }{ P° }\) = \(\frac { { n }_{ 2 } }{ { n }_{ 1 } }\)
W2 = 6.5g
W1 = 100g
Kb = 0.52
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-5
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-6

Question 13.
According to Raoult’s law, the relative Lowering of vapour pressure for a solution is equal to…
(a) mole fraction of solvent
(b) mole fraction of solute
(c) number of moles of solute
(d) number of moles of solvent
Answer:
(b) mole fraction of solute
Solution:
\(\frac { ∆P }{ P° }\) = x2 (Mole fraction of the solute)

Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions

Question 14.
At same temperature. which pair of the following solutions are isotonic?
(a) 0.2 M BaCl2 and 0.2M urea
(b) 0.1 M glucose and 0.2 M urea
(c) 0.1 MNaCl and 0.1 MK2SO4
(d) 0.1 MBa(NO3)2 and 0.1 MNa2 SO4
Answer:
(d) 0.1 M Ba (NO3)2 and 0.1 M Na2 SO4
Solution:
0.1 x 3 ion [Ba2 + 2NO3], 0.1 x 3 ion [2Na+, SO4]

The formula of normality a solution is the gram equivalent weight of a solute per liter of solution.

Question 15.
The empirical formula of a non-electrolyte(X) is CH2O. A solution containing six gram of X exerts the same osmotic pressure as that of 0.025 M glucose solution at the same temperature. The molecular formula of X is
(a) C2H4O2
(b) C8H16O8
(c) C4H8O4
(d) CH2O
Answer:
(b) C8H16O8
Solution:
1)non electrolute = (π2)glucose
C1RT = C2RT
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-7
\(\frac { 6 }{ n(30) }\) = 0.025
n = \(\frac { 6 }{ 0.025 x 30 }\) = 30
∴ Molecular formula C8H16O8

Question 16.
The KH for the solution of oxygen dissolved in water is 4 x 104 atm at a given temperature. If the partial pressure of oxygen in air is 0.4 atm, the mole fraction of oxygen in solution is …………..
(a) 4.6 x 103
(b) 1.6 x 104
(c) 1 x 10-5
(d) 1 x 105
Answer:
(c) 1 x 10-5
Solution:
KH = 4 x 104 atm,
(PO2)air = 0.4 atm,
(xo2)in solution = ?
air – in solution
(PO2)air = KH(xo2)in solution
0.4 = 4 x 104(xo2)in solution
(xo2)in solution = \(\frac { 0.4 }{ 4\times { 10 }^{ 4 } }\) = 1 x 10-5

Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions

Question 17.
Normality of 1.25M sulphuric acid is …………
(a) 1.25 N
(b) 3.75 N
(c) 2.5 N
(d) 2.25 N
Answer:
(c) 2.5 N
Solution:
Normality of H2SO4 = (No. of replacable H+) x M = 2 x 1.25 = 2.5 N

Question 18.
Two liquids X and Y on mixing gives a warm solution. The solution is …………..
(a) ideal
(b) non-ideal and shows positive deviation from Raoults law
(c) ideal and shows negative deviation from Raoults Law
(d) non – ideal and shows negative deviation from Raoults Law
Answer:
(d) non – ideal and shows negative deviation from Raoults Law
Solution:
∆Hmix is negative and show negative deviation from Raoults law.

Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions

Question 19.
The relative lowering of vapour pressure of a sugar solution in water is 3.5 x 10-3. The mole fraction of water in that solution is …………
(a) 0.0035
(b) 0.35
(c) 0.0035/18
(d) 0.9965
Answer:
(d) 0.9965
Solution:
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-9

Question 20.
The mass of a non-volatile solute (molar mass 80 g mol-1) which should be dissolved in 92g of toluene to reduce its vapour pressure to 90% ………..
(a) 10g
(b) 20g
(c) 9.2 g
(d) 8.89g
Answer:
(d) 8.89g
Solution:
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-10
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-11

Question 21.
For a solution, the plot of osmotic pressure (π) verses the concentration (e in mol L-1) gives a straight line with slope 310 R where ‘R’ is the gas constant. The temperature at which osmotic pressure measured is ………..
(a) 310 x 0.082 K
(b) 3 10°C
(c) 37°C
(d) \(\frac { 310 }{ 20.082}\)
Answer:
(c) 37°C
Solution:
π = CRT
y = x(m)
m = RT
310 R = RT
T = 310 K
= 37°C

Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions

Question 22.
200 ml of an aqueous solution of a protein contains 1 .26g of protein. At 300K, the osmotic pressure of this solution is found to be 2.52 x 10-3 bar. The molar mass of protein will be (R =0.083 Lhar mol-1 K-1) ……………
(a) 62.22 Kg mol-1
(b) 12444 g mol-1
(c) 300g mol-1
(d) none of these
Answer:
(a) 62.22 Kg mol-1
Solution:
π = CRT
M = \(\frac { WRT }{ π1 }\) = \(\frac { 1.26\times 0.083\times 300 }{ 2.52\times { 10 }^{ -3 }\times 0.2 }\) = 62.22Kg mol-1

Question 23.
The Van’t Hoff factor (i) for a dilute aqueous solution of the strong electrolyte barium hydroxide is ………..
(a) 0
(b) 1
(c) 2
(d) 3
Answer:
(b) 1
Solution:
Ba(OH)2 dissociates to form Ba2+ and 2OH-1 ion
α = \(\frac { (i – 1) }{ (n – 1) }\)
i = α (n – 1) + 1
n = i = 3 ( for Ba (OH)2, α = 1 )

Question 24.
What is the molality of a 10% w/w aqueous sodium hydroxide solution?
(a) 2.778
(b) 2.5
(c) 10
(a) 0.4
Answer:
(b) 2.5
Solution:
100% \(\frac { w }{ w }\) aqueous NaOH solution means that 10 g of sodium hydroxide in 100g solution.
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-13

Question 25.
The correct equation for the degree of an associating solute, ‘n’ molecules of which undergoes association in solution, is ………
(a) α = \(\frac { n(i – 1) }{ n – 1 }\)
(b) α2 = \(\frac { n(1 – i) }{ n – 1 }\)
(c) α = \(\frac { n(i – 1) }{ 1 – n }\)
(d) α = \(\frac { n(1 – i) }{ n(1 – i) }\)
Answer:
(c) α = \(\frac { n(i – 1) }{ 1 – n }\)
Solution:
α = \(\frac { (i – 1)n }{ (n – 1) }\) (or) \(\frac { n(i – 1) }{ (1 – n) }\)

Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions

Question 26.
Which of the following aqueous solutions has the highest boiling point?
(a) 0.1 M KNO3
(b) 0.1 M Na3PO4
(c) 0.1 M BaCl2
(d) 0.1 M K2SO4
Answer:
(a) 0.1 M KNO3
Solution:
Elevation of boiling point is more in the case of Na3PO4(no. of ions 4; 3 Na+, PO43-)

Question 27.
The freezing point depression constant for water is 1.86° k kg mo1-1 . If 5g Na2SO4 is dissolved in 45g water, the depression in freezing point is 3.64°C. The van’t Hoff factor for Na2SO4 is ……..
(a) 2.50
(b) 2.63
(c) 3.64
(d) 5.50
Answer:
(a) 2.50
Solution:
Kf = 1.86
W2 = 5g
∆Tf = 3.64
M2 = 142
W1 = 45g
ΔTf = i x Kf
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-14

Question 28.
Equimolal aqueous solutions of NaCI and KCI are prepared. If the freezing point of NaCI is – 2°C, the freezing point of KCI solution is expected to be ………
(a) – 2°C
(b) – 4°C
(c) – 1°C
(d) 0°C
Answer:
(a) – 2°C
(b) – 4°C
(c) – 1°C
(d) 0°C
Solution:
Equimolal aqueous solution of KCI also shows 2° C depression in freezing point.

Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions

Question 29.
Phenol dimerises in henzene having van’t Hoff factor 0.54. What is the degree of association?
(a) 0.46
(b) 92
(c) 46
(d) 0.92
Answer:
(d) 0.92
Solution:
α = \(\frac { (1-i)n }{ (n-1) }\) = \(\frac { (1 – 0.54)2 }{ (2 – 1) }\) = 0.46 x 2 = 0.92
Question 30.
Assertion: An ideal solution obeys Raoult’s Law
Reason: In an ideal solution, solvent-solvent, as well as solute-solute interactions, are similar to solute-solvent interactions.
(a) both assertion and reason are true and reason is the correct explanation of assertion
(b) both assertion and reason are true but reason is not the correct explanation of assertion
(c) assertion is true but reason is false
(d) both assertion and reason are false
Answer:
(a) both assertion and reason are true and reason is the correct explanation of assertion

Samacheer Kalvi 11th Chemistry Solutions Short Answer Questions

Question 31.
Define

  1. Molality
  2. Normality

Answer:
1. Molality (m):
It is defined as the number of moles of the solute present in 1 kg of the solvent
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-15

2. Normality (N):
It is defined as the number of gram equivalents of solute in I litre of the solution.
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-16

Question 32.
What is a vapour pressure of liquid? What is relative lowering of vapour pressure?
Answer:
1. The pressure of the vapour in equilibrium with its liquid ¡s called vapour pressure of the liquid at the given temperature.

2. The relative lowering of vapour pressure is defined as the ratio of lowering of vapour. pressure to vapour pressure of pure solvent. Relative lowering of vapour pressure
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-17

Question 33.
State and explain Henry’s law.
Answer:
“The partial pressure of the gas in vapor phase (vapour pressure of the solute) is directly proportional to the mole fraction (x) of the gaseous solute in the solution at low concentrations”. This statement is known as Henry’s law.
Henry’s law can be expressed as,
Psolute α xsolute in solution
Psolute = KH xsolute solution
Here, Psolute represents the partial pressure of the gas in vapour state which is commonly called vapour pressure. Xsolute in solution represents the mole fraction of solute in the solution. KH is an empirical constant with the dimensions of pressure.

Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions

Question 34.
State Raoult law and obtain expression for lowering of apour pressure when the nonvolatile solute is dissolved in solvent.
Answer:
Raoult’s law:
This law states that “in the case of a solution of volatile liquids the partial vapour pressure of each component (A & B) of the solution is directly proportional to its mole fraction.
PA ∝ x A
when xA = 1,
then k = P°A
(P°A = vapour pressure of pure component)
PA = P°A . xa
PB = P°B . xb
when a non-volatile is dissolved in pure water, the vapour pressure of the pure solvent will decrease. In such a solution, the vapours pressure of the solution will depend only on the solvent molecules as the solute is non-volatile.
Psolution ∝ xA
Psolution = k . xA
xA = 1, k = P°solvent
solution = P°solvent – Psolution
Lowering of vapour pressure = P°solvent – Psolution
Relative lowering of vapour pressure = \(\frac { P° – P }{ P° }\) = xB
where xB = Mole fraction of solute.

Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions

Question 35.
What is molal depression constant? Does it depend on nature of the solute?
Answer:
Kf = molar freezing point depression constant or cryoscopic constant.
∆Tf = Kf . m,
where
∆Tf = depression in freezing point.
m = molality of the solution
Kf = cryoscopic constant
If m = I
∆Tf = Kf
i.e., cryoscopic constant is equal to the depression in freezing point for 1 molal solution cryoscopic constant depends on the molar concentration of the solute particles. Kf is directly proportional to the molal concentration of the solute particles.
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-18
WB = mass of the solute
WA = mass of solvent
MB = molecular mass of the solute.

Question 36.
What is osmosis?
Answer:
“The phenomenon of the flow of solvent through a semipermeable membrane from pure solvent to the solution is called osmosis”. Osmosis can also be defined as “the excess pressure which must be applied to a solution to prevent the passage of solvent into it through the semipermeable membrane”. Osmotic pressure is the pressure applied to the solution to prevent osmosis.

Question 37.
Define the term isotonic
Answer:
1. Two solutions having same osmotic pressure at a given temperature are called isotonic solutions.

2. When such solutions arc separated by a semipermeable membrane, solvent flow between one to the other on either direction is same. i.e. the net solvent flow between two isotonic solutions is zero.

Samacheer Kalvi 11th Chemistry Solutions Long Answer Questions

Question 38.
You are provided with a solid ‘A’ and three solutions of A dissolved in water – one saturated, one unsaturated, and one supersaturated. How would you determine each solution?
Answer:
1. Saturated solution:
When the maximum amount of solute is dissolved in a solvent, any more addition of solute will result in precipitation at a given temperature and pressure. Such a solution is called a saturated solution.

2. Unsaturated solution:
When the minimum amount of solute is dissolved in a solvent at a given temperature and pressure is called an unsaturated solution.

3. Supersaturated solution:
It is a solution that holds more solute than it normally could in its saturated form.

Example:

  1. A saturated solution where the addition of more compound would not dissolve in the solution. 359 g of NaCI in 1 litre of water at 25°C.
  2. An unsaturated solution has the capacity to dissolve more of the compound. 36 g of NaCI in 1 litre of water at 25°C.
  3. A supersaturated solution is a solution in which crystals can start growing. 500 g of NaCI in 1 litre of water at 25°C.

Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions

Question 39.
Explain the effect of pressure on solubility.
Answer:
Generally, the change in pressure does not have any significant effect on the solubility of solids and liquids as they are not compressible. However, the solubility of gases generally increases with an increase in pressure.

Consider a saturated solution of a gaseous solute dissolved in a liquid solvent in a closed container. In such a system, the following equilibrium exists.
Gas (in a gaseous state) ⇌ Gas (in solution)

According to the Le-Chatelier principle, the increase in pressure will shift the equilibrium in the direction which will reduce the pressure. Therefore, more gaseous molecules dissolve in the solvent, and the solubility increases.

Question 40.
A sample of 12 M Concentrated hydrochloric acid has a density of 1.2 gL-1. Calculate the molality.
Answer:
Given:
Molarity = 12 M HCI
Density of the solution = 1.2 g L-1
In the 12 M HCl solution, there are 12 moles of HCl in 1 litre of the solution.
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-19
Calculate mass of water (solvent)
Mass of 1 litre HCI solution = density x volume
= 1.2gmL-1 x 1000 mL
= 1200g
Mass of LICI = No. of moles of HCI x molar mass of HCI
= 12mol x 36.5 g mol-1
= 438g
Mass of waler = mass of HCI solution – mass of HCI
Mass of waler = 1200 – 438 = 762 g
Molalily =\(\frac { 12 }{ 0.762 }\) = 15.75m

Question 41.
A 0.25 M glucose solution at 370.28 K has approximately the pressure as blood. What is the osmotic pressure of blood?
Solution.
C = 0.25 M
T = 370.28 K
(π)glucose = CRT
(π) = 0.25 mol L-1 × 0.082L atm K-1mol-1 × 370.28K
= 7.59 atm

Question 42.
Calculate the molarity of a solution containing 7.5g of glycine (NH2 – CH2 – COOH) dissolved in 500g of water.
Solution:
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-20

Question 43.
Which solution has the lower freezing point? 10g of methanol (CH3OH) in 100g of water (or) 20g of ethanol (C2H5HO) In 200g of water.
Solution:
∆Tf = Kf . m i.e. ∆Tf ∝ m
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-21
∴ Depression in freezing point is more in methanol solution and it will have a lower freezing point.

Question 44.
How many moles of solute particles are present in one litre of 10-4 M potassium sulphate?
Solution:
In 10-4M K2SO4 solution, there are 10-4 moles of potassium sulphate.
K2SO4 molecule contains 3 ions (2 K+ and 1SO42-)
1 mole of K2SO4 contains 3 x 6.023 x 1023 ions
10 mole of K2SO4 contains 3 x 6.023 x 102 x 10-4 ions = 18.069 x 1019

Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions

Question 45.
Henry’s law constant for solubility of methane in benzene is 4.2 x 10-5 mm Hg at a particular constant temperature. At this temperature, calculate the solubility of methane at

  1. 750 mm Hg
  2. 840 mmHg

Solution:
(KH)Benzene = 4.2 x 10-5 mm Hg. Solubility of methane = ? P = 750 mm Hg, p = 840 mm Hg
According to Henry’s Law,
P = KH . xsolution
750 mm Hg = 4.2 x 10-5 mm Hg . xsolution
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-24

Question 46.
The observed depression in the freezing point of water for a particular solution is 0.093°C. Calculate the concentration of the solution in molality. Given that the molal depression constant for water is 1.86 K kg mol-1.
Solution:
T1= 0.093°C = 0.093K
m = ?
Kf = 1.86K kg mol-1
∆Tf = kf . m
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-24

Question 47.
The vapour pressure of pure benzene (C6H6) at a given temperature is 640 mm Hg. 2.2 g of non-volatile solute is added to 40 g of benzene. The vapour pressure of the solution is 600 mm Hg. Calculate the molar mass of the solute?
Solution:
P0C6H6 = 640 mm Hg
W2 = 2.2 g (non volatile solute)
W1 = 40 g (benzene)
Psolution = 600 mm Hg
M2 = ?
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-25

Samacheer Kalvi 11th Chemistry Solutions In Text Questions – Evaluate Yourself

Question 1.
If 5.6 g of KOH is present in (a) 500 mL and (b) I litre of solution, calculate the molarity of each of these solutions.
Solution.
Mass of KOH = 5.6g
No. of moles = \(\frac { 5.6 }{ 5.6 }\) = 0.1 mol
1. Volume of the solution = 500 ml = 0.5 L

2. Volume of the solution = IL
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-26

3. Volume of the solution = IL
Molarity = \(\frac { 0.1 }{ 1 }\) M

Question 2.
2.82 g of glucose is dissolved in 30 g of water. Calculate the mole fraction of glucose and water.
Solution:
Mass of glucose = 2.82 g
No. of moles of glucose = \(\frac { 2.82 }{ 180 }\) = 0.0 16
Mass of water = 30g = \(\frac { 30 }{ 18 }\) = 1.67
xH2O = \(\frac { 1.67 }{ 1.67 + 0.016 }\) = \(\frac { 1.67 }{ 1.686 }\) = 0.99
xH2O + xglucose = 1
0.99 + xglucose = 1
xglucose = 1 – 0.99 = 0.01

Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions

Question 3.
The antiseptic solution of iodopovidone for the use of external application contains 10% w/v of iodopovidone. Calculate the amount of iodopovidone present in a typical dose of 1.5 mL.
Solution:
10% \(\frac { w }{ v }\) means that 10 g of solute in 100 ml solution
∴ Amount of iodopovidone in 1.5 ml = \(\frac { 10g }{ 100ml }\) x 1.5 ml = 0.15 g

Question 4.
A litre of sea water weighing about 1.05 kg contains 5 mg of dissohed oxygen (O2). Express the concentration of dissolved oxygen in ppm.
Solution:
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-28

Question 5.
Describe how would you prepare the following solution from pure solute and solvent

  1. 1 L of aqueous solution of 1.5 M COCI2.
  2. 500 mL of 6.0 % (v/v) aqueous methanol solution.

Solution:

  1. mass of 1.5 moles of COCI2 = 1.5 x 129.9 = 194.85g
  2. 194.85g anhydrous cobalt chloride is dissolved in water and the solution is make up to one litre in a standard flask.

Question 6.
How much volume of 6 M solution of NaOH is required to prepare 500 mL of 0.250 M NaOH solution.
Solution:
6% \(\frac { v }{ v }\) aqueous solution contains 6g of methanol in 100 ml solution. To prepare 500 ml of 6% v/v solution of methanol 30g methanol is taken in a 500 ml standard flask and required quantity of water is added to make up the solution to 500 ml.

Question 7.
Calculate the proportion of O2 and N2 dissolved in water at 298 K. When air containing 20% O2 and 80% N2 by volume is in equilibrium with water at 1 atm pressure. Henry’s law constants for two gases are KH(O2) = 4.6 x atm and KH (N2) 8.5 x 104 atm.
Solution:
C1V1 = C2V2
6M (V1) = 0.25M x 500 ml
V1 = \(\frac { 0.25 x 500 }{ 6 }\)
V1 = 20.3 mL

Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions

Question 8.
Explain why the aquatic species are more comfortable in cold water during winter season rather than warm water during the summer.
Solution:
Total pressure = 1 atm
PN2 = \((\frac { 80 }{ 100 })\) x Total pressure = \(\frac { 80 }{ 100 }\) x 1 atm = 0.8 atm
PO2 = \((\frac { 20 }{ 100 })\) x 1 = 0.2 atm
According to Henry’s Law
Psolute = KH x solute in solution
PN2 = (KH)Nitrogen x Mole fraction of Nitrogen in solution
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-29

Question 9.
Calculate the mole fractions of benzene and naphthalene in the vapour phase when an ideal liquid solution is formed by mixing 128 g of naphthalene with 39g of benzene. It is given that the vapour pressure of pure benzene is 50.71 mm Hg and the vapour pressure of pure naphthalene is 32.06 mm Hg at 300 K.
Solution:
P0pure benzene = 50.71 mm Hg
P0nepthalene = 32.06 mm Hg
Number of moles of benzene = \(\frac { 39 }{ 78 }\) = 0.5 mol
Number of moles of naphthalcne = \(\frac { 128 }{ 128 }\) =1 mol
Mole fraction of benzene = \(\frac { 0.5 }{ 1.5 }\) = 0.33
Mole fraction of naphthalene = 1 – 0.33 = 0.67
Partial vapour pressure of benzene =P0benzene x Mole fraction of benzene
= 50.71 x 0.33 = 16.73 mm Hg
Partial vapour pressure of naphthalene = 32.06 x 0.67 = 21.48mm Hg
Mole fraction of benzene in vapour phase = \(\frac { 16.73 }{ 16.73 + 21.48 }\) = \(\frac { 16.73 }{ 38.21 }\) = 0.44
Mole fraction of naphthalene in vapour phase = 1 – 0.44 = 0.56

Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions

Question 10.
Vapour pressure of a pure liquid A is 10.0 torr at 27°C. The vapour pressure is lowered to 9.0 torr on dissolving one grani of B in 20g of A. If the molar mass of A is 200 g mol-1 then calculate the molar mass of B.
Solution:
P0A = 10 torr
Psolution = 9 torr
WA = 20 g
WB = 1 g
MA = 200 g mol-1
MB = ?
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-30

Question 11.
2.56g of Sulphur is dissolved in 100g of carbon disuiphide. The solution boils at 319.692K. What is the molecular formula ofSulphur in solution? The boiling pointof CS2 is 319. 450K. Given that Kb for CS2 = 2.42 K kg mol-1
Solution:
W2 = 2.56g
W1 = 100g
T = 319.692 K
Kb = 2.42 K kg mol-1
∆Tb = (319.692 – 319.450) K = 0.242 K
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-31
M2 = 256g mol-1
Molecular mass of sulphur in solulion = 256 g mol-1
Atomic mass of one mole of sulphur atom = 32
No. of atoms in a molecule of sulphur = \(\frac { 256 }{ 32 }\) = 8
Hence, molecular tòrmula of sulphur is S8.

Question 12.
2g of a non-electrolyte solute dissolved in 75g of benzene lowered the freezing point of benzene by 0.20 K. The freezing point depression constant of benzene is 5.12 K Kg mol-1. Find the molar mass of the solute.
Solution:
W2 = 2g
W1 = 75g
∆Tf = 0.2 K
kf = 5.12 K kg mol-1
M2 = ?
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-32

Question 13.
What is the mass of glucose (C6H12O6) in its one-litre solution is isotonic with 6g L-1 of urea (NH2CONH2)?
Solution:
The osmotic pressure of urea solution (π1) = CRT
\(\frac { { W }_{ 2 } }{ { M }_{ 2 }V }\)RT = \(\frac { 6 }{ 60 x 1 }\) x RT
The osmotic pressure of glucose solution
2) \(\frac { { W }_{ 2 } }{ 180\times 1 }\) x RT
For isotonic solution, π1 = π2
\(\frac { 6 }{ 60 }\) = \(\frac { { W }_{ 2 } }{ 180\times 1 }\) RT
⇒ W2 = \(\frac { 6 }{ 60 }\) x 180
⇒ W2 = 18 g

Question 14.
0.2m aqueous solution of KCI freezes at – 0.68°C calculate van’t Hoff factor. Kf for water is 1.86 K kg mol-1.
Solution:
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-36
Given,
∆Tf = 0.680 K
m = 0.2 m,
∆Tf (observed) = 0.680K
∆Tf (Calculated) = kf
m = 1.86 K kg mol-1 x 0.2 mol kg-1 = 0.372K
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-37

Samacheer Kalvi 11th Chemistry Solutions Example problems Solved

Question 1.
What volume of 4M HCI and 2M HCI should be mixed to get 500 mL of 2.SM HCI?
Solution:
Let the volume of 4M HCl required to prepare 500 mL of 2.5 M HCI = x mL
Therefore, the required volume of 2M HCI = (500 – x) mL
We know from the equation x = \(\frac { 250 }{ 2 }\) = 125 mL
Hence, volume of 4M HCI required = 125 mL
Volume of 2M HCl required = (500 – 125) mL = 375 mL

Question 2.
0.24g of a gas dissolves in 1 L of water at 1.5 atm pressure. Calculate the amount of dissolved gas when the pressure is raised to 6.0 atm at constant temperature.
Solution:
Psolute = KH xsolute in solution
At pressure 1.5 atm, p1 = KH x1 ………..(1)
At pressure 6.0 atm, p2 = KHx2 …………..(2)
Dividing equation (1) by (2)
Weget
\(\frac { { P }_{ 1 } }{ { P }_{ 2 } }\) = \(\frac { { x }_{ 1 } }{ { x }_{ 2 } }\)
\(\frac { 1.5 }{ 6.0 }\) = \(\frac { { 0.24 } }{ { x }_{ 2 } }\)
Therefore
x2 = \(\frac { 0.24×6.0 }{ 1.5 }\) = 0.96 g/L

Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions

Question 3.
An aqueous solution of 2% nonvolatile solute exerts a pressure of 1.004 bar at the boiling point of the solvent. What is the molar mass of the solute when PA° is 1.013 bar?
Solution:
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-38
In a 2% solution weight of the solute is 2g and solvent is 98g
ΔP = PA0 – Psolution = 1.013 – 1.004 bar = 0.009 bar
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-39

Question 4.
0.75 g of an unknown substance is dissolved in 200 g solvent. If the elevation of boiling point is 0.15 K and molal elevation constant is 7.5K kg more then, calculate the molar mass of unknown substance.
Solution:
∆Tb = Kb m = Kb x W2 x 1000/M2 x W1
M2 = Kb x W2 x 1000/∆Tb x W1
= 7.5 x 0.75 x 1000/0.15 x 200 = 187.5g mol-1

Question 5.
Ethylene glycol (C2H6O2) can be used as an antifreeze in the radiator of a car. Calculate the temperature when ice will begin to separate from a mixture with 20 mass percent of glycol in water used in the car radiator. Kf for water = 1.86 K kg mol-1 and molar mass of ethylene glycol is 62g mol-1.
Solution:
Weight of solute (W2) = 20 mass percent of solution means 20g of ethylene glycol
Weight of solvent (water) W1 = 100 – 20 = 80g
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-40
The temperature at which the ice will begin to separate is the freezing of water after the addition of solute i.e. 7.5 K lower than the normal freezing point of water (273 – 7.5)K = 265.5K

Question 6.
At 400K 1.5 g of an unknown substance is dissolved in solvent and the solution is made to 1.5 L. Its osmotic pressure is found to be 0.3 bar. Calculate the molar mass of the unknown substance.
Solution:
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-41

Question 7.
The depression in freezing point is 0.24K obtained by dissolving 1g NaCI in 200g water. Calculate van’t – Hoff factor. The molal depression constant is 1.86 K kg mol-1.
Solution:
Sol. Molar mass of solute
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-42

Samacheer Kalvi 11th Chemistry Solutions Additional Questions Solved

Samacheer Kalvi 11th Chemistry Solutions 1 Mark Questions and Answers

I. Choose the correct answer.

Question 1.
Among the following, which one is mostly present in seawater?
(a) NaCI
(b) Nal
(c) KCI
(d) MgBr2
Answer:
(a) NaCI

Question 2.
Statement I: The most common property of seawater and air is homogeneity.
Statement II: The homogeneity implies uniform distribution of their constituents through the mixture.
(a) Statements I and II arc correct and II are the correct explanation of I.
(b) Statements I and II are correct but II is not the correct explanation of I.
(c) Statement I is correct but II is wrong.
(d) Statement I is wrong but II is correct.
Answer:
(a) statement I and II are correct and II is the correct explanation I.

Question 3.
Which one of the following is a homogeneous mixture?
(a) Seawater
(b) Air
(c) Alloys
(d) All the above
Answer:
(d) All the above

Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions

Question 4.
Statement I: The salt solution is an aqueous solution.
Statement II: If water is used as the solvent, the resultant solution is called an aqueous solution.
(a) Statements I and II are correct but II is not the correct explanation of I.
(b) Statements I and II are correct and II is the correct explanation of I.
(c) Statement I is correct but statement II is wrong.
(d) Statement I is wrong but statement II is correct.
Answer:
(b) Statements I and II are correct and II is the correct explanation of I.

Question 5.
Statement I: The dissolution of ammonium nitrate increases steeply with an increase in temperature.
Statement II: The dissolution process of ammonium nitrate is endothermic in nature.
(a) Statement I and II are correct and statement II is the correct explanation of statement I.
(b) Statement I and II are correct but II is not the correct explanation of I.
(c) Statement I is correct but II is wrong.
(d) Statement I is wrong but II is correct.
Answer:
(a) Statement I and II are correct and statement II is the correct explanation of statement I.

Question 6.
In which of the following compound the solubility decreases with the increase of temperature?
(a) sodium chloride
(b) ammonium nitrate
(c) ceric sulphate
(d) calcium chloride
Answer:
(c) ceric sulphate

Question 7.
Which of the following is not an ideal solution?
(a) Benzene & toluene
(b) n – Hexane & n – Heptane
(c) Ethyliodide & ethyl bromide
(d) Ethanol and water
Answer:
(d) Ethanol and water

Question 8.
Which one of the following shows positive deviation from Raoult’s law?
(a) Ethyliodide and Ethyl bromide
(b) Ethyl alcohol and cyclohexane
(c) Chioro benzene & bromo benzene
(d) Benzene & toluenc
Answer:
(b) Ethyl alcohol and cyclohexane

Question 9.
Which one of the following is not a non-ideal solution showing positive deviation?
(a) Benzene & acetone
(b) CCl4 & CHCl3
(c) Acetone & ethyl alcohol
(d) Benzene and toluene
Answer:
(d) Benzene and toluene

Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions

Question 10.
Which of the following shows a negative deviation from Raoult’s law?
(a) Phenol and aniline
(b) Benzene and toluene
(c) Acetone and ethanol
(d) Bcnzene and acetone
Answer:
(a) Phenol and aniline

Question 11.
Which of the following is not a non-ideal solution showing negative deviation?
(a) Phenol and aniline
(b) Ethanol and water
(c) Acetone + Chloroform
(d) n – Heptane and n – Hexane
Answer:
(d) n – Heptane and n-Hexane

Question 12.
Statement I: A solution of potassium chloride in water deviates from ideal behavior.
Statement II: The solute dissociates to give K and Cl ions which form strong ion-dipole interaction with water molecules.
(a) Statement I & II are correct and II is the correct explanation of I
(b) Statement I & II are correct but II is not the correct explanation of I
(c) Statement I is correct but statement II is wrong.
(d) Statement I is wrong but statement II is correct.
Answer:
(a) Statement I & II are correct and II is the correct explanation of I

Question 13.
Statement I: Acetic acid deviates from ideal behavior.
Statement II: Acetic acid exists as a dimer by forming intermolecular hence deviates from Raoult’s law.
(a) Statement I & II are correct and II is the correct explanation of I.
(b) Statement I & II are correct but II is not the correct explanation of I.
(c) Statement I is true but II is wrong.
(d) Statement I is wrong but II is correct.
Answer:
(a) Statement I & II are correct but II is the correct explanation of I.

Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions

Question 14.
Which one of the following has found to have abnormal molar mass? hydrogen bonds and
(a) NaCl
(b) KCI
(c) Acetic acid
(d) all the above
Answer:
(d) All the above

Question 15.
What would be the value of the van’t Hoff factor for a dilute solution of K2SO4 in water?
(a) 3
(b) 2
(c) 1
(d) 4
Answer:
(a) 3
Solution:
ions produced = n = 3
Since
K2SO4 → 2K+ + SO42-
K2SO4 is completely dissociated so
∝ = \(\frac { i – 1 }{ n – 1 }\) = \(\frac { i – 1 }{ 3 – 1 }\) = 1
i – 1 = 1 x 2
i – 1 = 2
i = 2+1 = 3

Question 16.
In the determination of the molar mass of AB using a colligative property, what may be the value of van’t Hoff factor if the solute is 50% dissociates?
(a) 0.5
(b) 1.5
(c) 2.5
(d) 1
Answer:
(b) 1.5
Solution:
∝ = \(\frac { i – 1 }{ n – 1 }\) = 0.5
\(\frac { i – 1 }{ 2 – 1 }\) = 0.5
i – 1 = 0.5
i = 0.5 + 1 = 1.5

Question 17.
Which of the following solution has the highest boiling point?
(a) 5.85% solution of NaCI
(b) 18.0% solution of glucose
(c) 6.0% solution of urea
(d) All have the same boiling point
Answer:
(a) 5.85% solution of NaCl

Question 18.
Which one of the following pair is called an ideal solution?
(a) nicotine – water
(b) water – ether
(c) water – alcohol
(d) Chiorobenzene – bromobenzene
Answer:
(d) Chiorobenzene – bromobenzene

Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions

Question 19.
Which of the following is not a colligative property?
(a) optical activity
(b) osmotic pressure
(c) elevation boiling point
(d) depression in freezing point
Answer:
(a) optical activity

Question 20.
On dissolving sugar in water at room temperature solution feels cool to touch. Under which of the following cases dissolution of sugar will be most rapid?
(a) Sugar crystals in cold water
(b) Sugar crystals in hot water
(c) powdered sugar in cold water
(d) powdered sugar in hot water
Answer:
(d) powdered sugar in hot water

II. Match the following.
Question 1.
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-43
Answer:
(a) 3 4 1 2

Question 2.
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-44
Answer:
(d) 3 4 2 1

Question 3.
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-45
Answer:
(c) 2 4 1 3

Question 4.
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-46
Answer:
(a) 4 3 1 2

Question 5.
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-47
Answer:
(b) 2 4 1 3

III. Fill in the blanks.

Question 1.
……… covers more than 70% of the earth’s surface.
Answer:
Seawater

Question 2.
……… is an important naturally occurring solution.
Answer:
Air

Question 3.
An example of solid homogeneous mixture is ……….
Answer:
Brass

Question 4.
A mixture of N2, O2, CO2 and other traces of gases is known as ………
Answer:
Air

Question 5
……… a non – aqueous solution.
Answer:
Br2 in CCl4

Question 6.
……… is an example of a gaseous solution.
Answer:
Camphor in nitrogen gas

Question 7.
……… is used for a dental filling.
Answer:
Amalgam of potassium

Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions

Question 8.
Carbonated water is an example for ………
Answer:
Liquid solution

Question 9.
Humid oxygen is an example of ………
Answer:
Gaseous solution

Question 10.
The concentration of commercially available H2O2 is ………
Answer:
3%

Question 11.
The molality of the solution containing 45g of glucose dissolved in 2kg of water is ………
Answer:
0.125m
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-48

Question 12.
5.845 g of NaCl is dissolved in water and the solution was made up to 500 mL using a standard flask. The strength of the solution in molarity is ………
Answer:
0.2 M
Solution:
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-49

Question 13.
3.15 g of oxalic acid dihydrate is dissolved in water and the solution was made up to 100 ml using a standard flask. The strength of the solution in normality is ………
Answer:
0.5N
Solution:
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-50

Question 14.
5.85 g of NaCl is dissolved in water and the solution was made upto 500 ml using a standard flask. The strength of the solution in formality is ………
Answer:
0.2 F
Solution:
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-51

Question 15.
Neomycin, aminoglycoside antibiotic cream contains 300 mg of neomycin sulphate the active ingredient in 30 g of ointment base. The mass percentage of neomycin is ………
Answer:
1%
Solution:
The mass percentage of neomycin
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-52

Question 16.
0.5 mole of ethanol is mixed with 1.5 moles of water. Then the mole fraction of ethanol and water are ……….
Answer:
0.25, 0.75
Solution:
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-53
= \(\frac { 0.5 }{ 1.5 + 0.5 }\) = \(\frac { 0.5 }{ 2.0 }\) = 0.25
Mole fraction of water = \(\frac { 1.5 }{ 2.0 }\) = 0.75

Question 17.
50 mL of tincture of benzoin, an antiseptic solution contains 10 ml of benzoin. The volume percentage of benzoin is ……….
Answer:
20%
Solution:
Volume percentage of benzoin
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-54
= \(\frac { 10 }{ 50 }\) x 100 = 20%

Question 18.
A 60 ml of paracetamol pediatric oral suspension contains 3g of paracetamol. The mass percentage of paracetamol is …………
Answer:
5%
Solution:
Mass percentage of paracetamol =
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-55
= \(\frac { 3 }{ 60 }\) x 100 = 5%

Question 19.
50 ml of tap water contains 20 mg of dissolved solids. The TDS value in ppm is ………..
Answer:
400 ppm
Solution:
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-56

Question 20.
The concentration term used in the neutralisation reactions is …………
Answer:
Normality

Question 21.
The concentration term is used in the calculation of vapour pressure of the solution is …………..
Answer:
Mole fraction

Question 22.
The term used to express the active ingredients present in therapeutics is ………
Answer:
Percentage units

Question 23.
When the maximum amount of solute is dissolved in a solvent at a given temperature, the solution is called ………..
Answer:
Saturated solution

Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions

Question 24.
The solvent in which sodium chloride readily dissolves is …………
Answer:
Water

Question 25.
………… is used by deep-sea divers.
Answer:
Helium, nitrogen and oxygen

Question 26.
The mathematical expression of Raoult’s law is ………..
Answer:
PA = PA0 . XA

Question 27.
……….. is an ideal solution?
Answer:
Chloro benzene & bromo benzene

Question 28.
………….. is important in some vital biological systems.
Answer:
osmotic pressure

Question 29.
………. is not a colligative property.
Answer:
vapour pressure

Question 30.
According to van’t Hoff equation. the value of osmotic pressure t is equal to …………
Answer:
π = CRT

Question 31.
The osmotic pressure of the blood cells is approximately equal to 37°C.
Answer:
7 atm.

Question 32.
Which one of the following is applied in water purification?
Answer:
reverse osmosis

Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions

Question 33.
In the commercial reverse osmosis process, the semi-permeable membrane used is ………..
Answer:
cellulose acetate

Question 34.
The degree of dissociation α is equal to ……….
Answer:
\(\frac { i – 1 }{ n – 1 }\)

Question 35.
The degree of association a is equal to ……….
Answer:
\(\frac { (i – 1)n }{ n – 1 }\)

Question 36.
The estimated vantt Hoff factor for acetic acid solution in benzene is ………..
Answer:
0.5

Question 37.
The estimated van’t Hoff factor for sodium chloride in water is ………..
Answer:
2

Question 38.
Number of moles of the solute dissolved per dm3 of solution is ……….
Answer:
molarity

Question 39.
Molarity of pure water is ………….
Answer:
55.55
Solution:
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-57
Question 40.
18 g of glucose is dissolved in 90 g of water. The relative lowering of vapour pressure is equal to ………..
Answer:
0.1
Solution:
\(\frac { P° – P }{ P° }\) = x2
x2 = No. of moles of glucose
\(\frac { 18 }{ 180 }\) = 0.1
\(\frac { P° – P }{ P° }\) = 0.1

Question 41.
When NaCl is dissolved in water, boiling point ………..
Answer:
increases

Question 42.
Use of glycol as antifreeze in an automobile is an important application of …………….
Answer:
Colligative property

Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions

Question 43.
Ethylene glycol is mixed with water and used as antifreeze in radiators because …………..
Answer:
it lowers the freezing point of water

Question 44.
The colligative properties of a solution depend on ………… present in it.
Answer:
Number of solute particles

Question 45.
Low concentration of oxygen in the blood and tissues of people living at high altitude is due to ………….
Answer:
low atmospheric pressure

IV. Choose the odd one out.

Question 1.
(a) Air
(b) Camphor in nitrogen gas
(c) Humid oxygen
(d) Saltwater
Answer:
(d) Saltwater.
a, b and e are gaseous solutions whereas d is a liquid solution.

Question 2.
(a) CO2 dissolve in water
(b) Saltwater
(c) Solution of H2 in palladium
(d) Ethanol dissolved in water
Answer:
(c) Solution of H2 in palladium
a, b and d are liquid solutions whereas c is a solid solution.

Question 3.
(a) Amalgam of potassium
(b) Camphor in nitrogen gas
(c) Solution of H2 in palladium
(d) Gold alloy
Answer:
(b) Camphor in nitrogen gas
a, b and d arc solid solutions whereas b is the gaseous solution.

Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions

Question 4.
(a) Vapour pressure
(b) Lowering of vapour pressure
(c) Osmotic pressure
(d) Elevation of boiling point
Answer:
(a) Vapour pressure
b, e and dare colligative properties whereas a is a physical property.

Question 5.
(a) Benzene and tolucne
(b) Chlorobenzene and Bromobenzene
(c) Benzene and acetone
(d) n – hexane and n – heptane
Answer:
(a) Benzene and acetone
a, b, and d are ideal solutions whereas c is a non-ideal solution.

Question 6.
(a) Ethyl alcohol and cyclohexane
(b) Ethyl bromide and ethyl iodide
(c) Acetone and ethyl alcohol
(d) Benzene and acetone
Answer:
(a) Ethyl bromide and ethyl iodide
a, e and dare non-ideal solutions whereas b is an ideal solution.

V. Choose the correct pair.

Question 1.
(a) Humid oxygen – Liquid solution
(b) Gold alloy – Solid solution
(c) Saltwater – Gaseous solution
(d) Solution of H2 in palladium – Gaseous solution
Answer:
(b) Gold alloy – Solid solution

Question 2.
(a) Air – Gaseous solution
(b) Amalgam of potassium – Liquid solution
(c) Saltwater – Solid solution
(d) Carbonated water – Solid solution
Answer:
(a) Air – Gaseous solution

Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions

Question 3.
(a) Benzene and toluene – Non-ideal solution
(b) Benzcnc and acetone – Non-ideal solution
(c) Chlorobenzene and bromo henzene – Non-ideal solution
(d) Carbon tetrachloride and Chloroform – the ideal solution
Answer:
(b) Benzene and acetone – Non-ideal solution

Question 4.
(a) Benzene and toluene – Ideal solution
(b) n-hexane and n-heptane – Non-ideal solution
(c) Ethyl iodide and ethyl bromide – Non-ideal solution
(d) Chiorobenzene and bromo benzene – Non-ideal solution
Answer:
(a) Benzene and toluene – Ideal solution

VI. Choose the incorrect pair.
Question 1.
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-59
Answer:
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-60

Question 2.
(a) Benzene and acetone – Ideal solution
(b) Ethyl alcohol and cyclohexane – Non-ideal solution
(C) n-hexane and n-heptane – Ideal solution
(d) Chioro benzene – Ideal solution
Answer:
(a) Benzene and acetone – Ideal solution

VII Assertion & Reason.

Question 1.
Assertion (A): When NaCI is added to water, depression in the freezing point is observed.
Reason (R): The lowering of vapour pressure of a solution causes the depression in freezing point.
(a) Assertion and Reason are correct and R is the correct explanation of A.
(b) Both A and R are correct but R is not the correct explanation of A.
(c) A is correct but R is wrong
(d) A is wrong but R is correct
Answer:
(a) Assertion and Reason are correct and R is the correct explanation of A.

Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions

Question 2.
Assertion (A): Ammonia reacts with water does not obey Henry’s law.
Reason (R): The gases reacting with the solvent does not obey Henry’s law.
(a) Both (A) and (R) are correct and (R) is the correct explanation of (A).
(b) Both (A) and (R) are correct but (R) is not the correct explanation of (A).
(c) (A) is correct hut (R) is wrong.
(d) (A) is wrong but (R) is correct.
Answer:
(a) Both (A) and (R) are correct and (R) is the correct explanation of (A).

Question 3.
Assertion (A): Acetic acid solution deviates from Raoult’s law.
Reason (R): Association of solute molecules exists as a dimer by forming intermolecular. hydrogen bonds and hence deviates from Raoult’s law.
(a) Both (A) and (R) arc wrong.
(b) Both (A) and (R) are correct and (R) is the correct explanation of (A).
(c) (A) is correct but (R) is wrong.
(d) (A) is wrong but (R) is correct.
Answer:
(b) Both (A) and (R) are correct and (R) is the correct explanation of (A).

VIII. Choose the correct statement.

Question 1.
(a) Raoult’s law is applicable to volatile solid solute in liquid solvent
(b) Henry’s law is applicable to solution containing solid solute in liquid solvent
(c) For very dilute solutions, the solvent obeys Raoult’s law and the solute obeys Henry’s law.
(d) For saturated solution containing volatile solid solute in liquid solvent both laws are obeyed.
Answer:
(c) For very dilute solutions. the solvent obeys Raoult’s law and the solute obeys LIenrys law.

Samacheer Kalvi 11th Chemistry Solutions 2 Marks Questions and Answers

I. Write brief answer to the following questions:

Question 1.
Define solution.
Answer:
A solution is a homogeneous mixture of two or more substances, consisting of atoms, ions or molecules. The constituent of the homogeneous mixture present in a lower amount is called the solute, and the one present in a larger amount is called the solvent. For example, when a small amount of NaCl dissolved in water.

Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions

Question 2.
Define the solution with an example.
Answer:
1. A solution is a homogeneous mixture of two or more substances consisting of atoms. ions or molecules.

2. For example, when a small amount of NaCl is dissolved in water, a homogeneous solution is obtained. In this solution, Na+ and C ions are uniformly distributed in the water. Here NaCI is the solute and water is the solvent.

Question 3.
What is an unsaturated solution?
Answer:
An unsaturated solution is one that contains less amount of solute than its capacity to dissolve.

Question 4.
Define molality.
Answer:
Molality is defined as the number of moles of solute present in 1 kg of the solvent.
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-61

Question 5.
Define molarity.
Answer:
Molarity is defined as the number of moles of solute present in 1 litre of the solution.
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-62

Question 6.
Define normality.
Answer:
Normality is defined as the number of gram equivalents of solute present in 1 litre of the solution.
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-63

Question 7.
Define formality.
Answer:
Formality (F) is defined as the number of formula weight of solute present in 1 litre of the solution.
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-64

Question 8.
Define mole fraction.
Answer:
The mole fraction of a component is the ratio of a number of moles of the component to the total number of moles of all components present in the solution.
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-65

Question 9.
Show that the sum of mole fraction of a solution is equal to one.
Answer:
Consider a solution containing two components A and 13 whose mole fractions are xA and xB respectively. Let the number of moles of two components A and B are nA and nB respectively.
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-66

Question 10.
Define mass percentage.
Answer:
Mass percentage is defined as the ratio of the mass of the solute in g to the mass of solution in g multiplied by 100.
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-67

Question 11.
Define volume percentage.
Answer:
Volume percentage is defined as the ratio of volume of solute in mL to the volume of solution in ml multiplied by 100.
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-68

Question 12.
Define mass by volume percentage.
Answer:
It is defined as the ratio of the mass of the solute in g to the volume of the solution in ml multiplied by 100.
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-69

Question 13.
What is meant by ppm? Where is it used?
Answer:
1. part per million =
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-70

2. ppm is used to express the quantity of solutes present in small amounts in solutions.

Question 14.
What is the elevation of boiling point? Give it.
Answer:
The temperature difference between the solution and pure solvent is called elevation of boiling point,
∆Tb = T – T°
Unit of ∆Tb is K Kg mole-1.

Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions

Question 15.
Define solubility.
Answer:
The solubility of a substance is defined as the amount of the solute that can be dissolved in loo g of the solvent at a given temperature to form a saturated solution.

Question 16.
Ammonia is more soluble than oxygen in water. Why?
Answer:
Ammonia forms hydrogen bonding with water molecules, this intermolecular bonds arc very strong and thus the ammonia is more soluble in water. Ammonia is strongly interact with water to form ammonium hydroxide. But oxygen is more electronegative it is not able to interact with water more. So NH3 is more soluble than O2 in water.

Question 17.
Solubility of a solid solute in a liquid solvent increases with increase in temperature. Justify this statement.
Answer:
When the temperature is increased,the average kinetic energy of the molecules of the solute and the solvent increases. The increase in the kinetic energy facilitates the solvent molecules to break the intermolecular attractive forces that keep the solute molecules together and hence the solubility increases.

Question 18.
Dissolution of ammonium nitrate increases with increase in temperature. Why?
Answer:
The dissolution process of ammonium nitrate is endothermic. So the solubility increases with increase in temperature.

Question 19.
What is the relationship between the solubility of eerie sulphate with temperature?
Answer:
The dissolution of eerie sulphate is exothermic and the solubility decreases with the increase in temperature.

Question 20.
Why in the dissolution of CaCl2, the solubilit increases moderately with high temperature?
Answer:
Even though the dissolution of CaCI2, is cxothcrmic, the soluhility increases moderately with increase in temperature. Here the entropy factor plays a significant role in deciding the position of equilibrium.

Question 21.
Why the carbonated drinks are stored in pressurized container?
Answer:
1. The carbonated beverages contain CO2 dissolved in them. To dissolve the CO2 in these drinks, CO2 gas is bubbled through them under high pressure.

2. These containers are sealed to maintain the pressure. When we open these containers at atmospheric pressure, the pressure of the CO2 drops to the atmospheric pressure level and hence bubbles of CO2 rapidly escape from the solution and show effervescence.

Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions

Question 22.
Define

  1. Evaporation
  2. Condensation.

Answer:
1. Evaporation:
If the kinetic energy of molecules in the liquid state overcomes the intermolecular force of attraction between them, then the molecules will escape from the liquid state. This process is called evaporation.

2. Condensation:
The vapour molecules are in random motion during which they collide with each other and also with the walls of the container. As the collision is inelastic, they lose their energy and as a result, the vapour returns back to a liquid state. This process is called condensation.

Question 23.
State Dalton’s law of partial pressure.
Answer:
According to Dalton’s law of partial pressure, the total pressure in a closed vessel will be equal to the sum of the partial pressure of the individual components.
Ptotal = PA + PB

Question 24.
Give the reason behind the lowering of vapour pressure in the dissolution of NaCl in water?
Answer:
NaCI is a non volatile solute. When a non-volatile solute is dissolved in a pure solvent, the vapour pressure of pure solvent will decrease. In such a solution, vapour pressure of the solution will depend only on the solvent molecules as the solute is non-volatile.

Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions

Question 25.
What is the ideal solution? Give example.
Answer:
An ideal solution is a solution in which each component i.e., the solute as well as the solvent obeys Raoult’s law over the entire range of concentration.

Question 26.
What is volume percentage?
Answer:
It is defined as the volume of the component present in 100mL of the solution. If Va is a volume of solute and Vb is the volume of solvent, then
Vollume percentage of solute = \(\frac{V_{a} \times 100}{V_{a}+V_{b}}\)

Question 27.
What are colligative properties? Give example.
Answer:
The properties which do not depend on the chemical nature of the solute but depend only on the number of solute particles present in the solution are called colligative properties. e.g.,

  1. Relative lowering of vapour pressure – \(\frac { P° – P}{ P° }\)
  2. Osmotic pressure – π
  3. Elevation of the boiling point – ∆Tb
  4. Depression in freezing point – ∆Tf

Question 28.
What is meant by elevation of boiling point?
Answer:
1. The boiling point of a liquid is the temperature at which its vapour pressure becomes equal to the atmospheric pressure.

2. When a non-volatile solute is added to pure solvent at its boiling point, the vapour pressure of the solution is lowered below 1 atm. To bring the vapour pressure again to 1 atm, the temperature of the solution has to be increased.

3. As a result, the solution boils at a higher temperature (Tb) than the boiling point of pure solvent (Tb°). This increase in the boiling point is known as the elevation of boiling point.

Question 29.
Define ebullioscopic constant.
Answer:
Ebullioscopic constant kb, is equal to the elevation in boiling point for 1 molal solution.
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-71

Question 30.
What is Van’t Hoff factor?
Answer:
It is defined as the ratio of the actual molar mass to the abnormal (calculated) molar mass of the solute. Here, the abnormal molar mass is the molar mass calculated using the experimentally determined colligative property.
i = \(\frac{\text { Normal (actual) molar mass }}{\text { obseved (abnormal) molar mass }}\)

Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions

Question 31.
Write the Van’t Hoff equation of osmotic pressure.
Answer:
Van’t Hoff equation states that for dilute solutions, the osmotic pressure is directly proportional to the molar concentration of the solute and the temperature of the solution.
π = CRT
where
π = Osmotic pressure
C = concentration
T = Temperature
R = gas constant

Question 32.
Define Van’t Hoff factor.
Answer:
van’t Hoff factor (I) is defined as the ratin of the actual molar mass to the abnormal molar mass of the solute.
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-72

Question 33.
How is degree of dissociation and degree of association are related with van’t Hoff factor?
Answer:
The degree of dissociation or association can be related to van’t Hoff factor
1. using the following relationship

  • αdissociation = \(\frac { i – 1 }{ n – 1 }\)
  • αassociation = \(\frac { (1 – i)n }{ n – 1 }\)

where n = number of solute particles

Question 34.
Give an example of a solid solution ¡n which the solute is a gas.
Answer:
Solution of hydrogen in palladium.

Question 35.
Why the carbonated drinks are stored in a pressurized container?
Answer:
The carbonated beverages contain carbon dioxide dissolved in them. To dissolve the carbon dioxide in these drinks, the CO2 gas is bubbled through them under high pressure. These containers are sealed to maintain the pressure. When we open these containers at atmospheric pressure, the pressure of the CO2 drops to the atmospheric level, and hence bubbles of CO2 rapidly escape from the solution and show effervescence. The burst of bubbles is even more noticeable if the soda bottle in warm condition.

Question 36.
Why do gases always tend to be less soluble in liquids as the temperature is raised?
Answer:
Mostly dissolution of gases in liquid is an exothermic process. it is because of the fact that this process involves a decrease of entropy. Thus, an increase in temperature tends to push the equilibrium towards a backward direction as a result of which solubility of the gas decrease with a rise in temperature.
(Gas + Solvent \(\rightleftharpoons\) Solution + Heat)

Question 37.
Why is the freezing point depression of 0.1 M NaCl solution nearly twice that of 0.1M glucose solution?
Answer:
NaCl is an electrolyte and it dissociates completely whereas glucose being a non-electrolyte does not dissociate. Hence, the number of particles in 0.1 M NaCl solution is nearly double for NaCI solution than that for glucose solution of same molarity.

Therefore depression in freezing point being a colligative property ¡s nearly twice for NaCl solution than that for glucose solution of same molarity.

Question 38.
Why a person suffering from high blood pressure is advised to take a minimum quantity of common salt?
Answer:
Osmotic pressure is directly proportional to the concentration of solutes. Our body fluid contains a number of solutes. On taking large amount of salt, ions entering into the body fluid thereby raises the concentration of solutes. As a result, osmotic pressure increases which may rupture the blood cells.

Samacheer Kalvi 11th Chemistry Solutions 3 Marks Questions and Answers

Question 1.
What are gaseous solution? Give its various types with example
Answer:
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-73

Question 2.
What are liquid solutions ? Explain with example
Answer:
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-74

Question 3.
What are solid solution? Give example.
Answer:
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-75

Question 4.
How will you prepare a standard solution?
Answer:

  1. A standard solution or a stock solution is a solution whose concentration is accurately known.
  2. A standard solution of required concentration can be prepared by dissolving a required amount of a solute in a suitable amount of solvent.
  3. It is done by transforming a known amount of solute to a standard flask of definite volume. A small amount of water is added lo the flask and shaken well to dissolve the salt.
  4. Then water is added to the flask to bring the solution level lo the mark indicated at the top end of the flask.
  5. The flask is stoppered and shaken well to make concentration uniform.

Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions

Question 5.
What are the advantages of standard solution.
Answer:
1. The error due to weighing the solute can be minimised by using concentrated stock solution that requires large quantities of solute.

2. We can prepare working standards of different concentrations by diluting the stock solution which is more efficient since consistency is maintained.

3. Some of the concentrated solutions are more stable and are less likely to support microbial growth than working standards used in the experiments.

Question 6.
Explain the solubilities of ammonium nitrate, calcium chloride, ceric sulphate and sodium chloride in water at different temperature with a graph.
Answer:
1. The solubility of sodium chloride does not vary appreciably as the maximum solubility is achieved at normal temperature. In fact, there is only 10% increase in solubility between 0°C to 100°C.

2. The dissolution process of ammonium nitrate is endothermic, the solubility increases with

3. In the case of eerie sulphate. the dissolution is exothermic and the solubility decreases with increase in temperature.

4. Even though the dissolution of calcium chloride is exothermic, the solubility increases moderately with increase in temperature. Here the entropy factor also plays a significant role in deciding the position of equilibrium.
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-76

Question 7.
Explain the effect of temperature gaseous solute ¡n liquid solvent.
Answer:
1. In the case of gaseous solute in liquid solvent, the solubility decreases with increase in temperature.

2. When a gaseous solute dissolves in a liquid solvent, its molecules interact with solvent molecules with weak inter molecular forces when the temperature increases, the average. kinetic energy of the molecules present in the solution also increases.

3. The increase in kinetic energy breaks (he weak inter molecular forces between the gaseous solute and liquid solvent with results in the release of the dissolved gas molecules to gaseous state.

4. The dissolution of most of the gases in Liquid solvents is an endothermic process, the increase in temperature decreases the dissolution of gaseous molecules.

Question 8.
Give reason why aquatic species are less sustained in hot water?
Answer:
There will be decrease in solubility of gases in solution with increase in temperature. During summer, in hot water rivers, due to high temperature. the availability of dissolved oxygen decreases. So the aquatic species are less sustained in hot water.

Question 9.
Deep – sea divers use air diluted with helium gas in their tanks. Why? (or) Justify this statement.
Answer:
1. Deep-sea divers carry a compressed air tank for breathing at high pressure under water. This air tank contains nitrogen and oxygen which are not very soluble in blood and other body fluids at normal pressure.

2. As the pressure at the depth is far greater than the surface atmospheric pressure, more nitrogen dissolves in the blood when the diver breathes from tank.

3. When the divers ascends to the surface, the pressure decreases, the dissolved nitrogen comes out of the blood quickly forming bubbles in the blood stream.

These bubbles restrict blood flow, affect the transmission of nerve impulses and can even burst the capillaries or block them. This condition is called “the bends” which are painful and dangerous to life.

4. To avoid such dangerous condition they use air diluted with helium gas (11.7 % helium, 56.2% nitrogen and 32.1% oxygen) of lower solubility of helium in the blood than nitrogen.

Question 10.
What are the limitations of Henry’s law?
Answer:

  1. Henry’s law is applicable at moderate temperature and pressure only.
  2. Only the less soLuble gases obey Henry’s law.
  3. The gases reacting with solvent do not obey Henry’s law.
  4. The gases obeying Henrys law should not be associated or dissociated while dissolving in the solvent.

Question 11.
Explain how benzene in toluene obeys Raoult’s law.
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-77
Answer:
The variation of vapour pressure of pure benzene and toluenc with its mole fraction is given in the graph.
1. The vapour pressure of pure toluene and pure benzene are 22.3 and 74.7 mm Hg respectively.

2. The graph shows the partial vapour pressure of pure components increases linearly with the increase of the mole fraction of the respective components. The total pressure at any composition of the solute and solvent is given by the straight line.

3. Psolution = P0toluene + xbenzene (P0benzene – P0toluene)

Question 12.
Derive the relationship between the relative lowering of vapour pressure and mole fraction of the solute.
Answer:
Psolution ∝ xA by Raoult’s law. where xA is the mole fraction of the solvent.
Psolution = k . xA
When
xA = 1
k = P0solvent
P0solvent = partial pressure of pure solvent
Psolution = P0solvent . xA
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-78
where
xB = mole fraction of the solute
xA + xB = 1
xB = 1 – xA
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-79

Question 13.
The depression in freezing point is 0.24 K obtained by dissolving 1 g NaCl in 200g water. Calculate van’t – Hoff factor. The molar depression constant in 1.86 K Kg mol-1
Solution :
Molar mass of solute = \(\frac{1000 \times K_{f} \times \text { mass of } N a C l}{\Delta T_{f} \times \text { mass of solvent }}\)

= \(\frac{1000 \times 1.86 \times 1}{0.24 \times 200}\)
= 38.75 g mol-1

Theoretical molar mass of NaCl is = 58.5 g mol-1

i = \(\frac{\text { Theoretical molar mass }}{\text { Experimental molar mass }}\)
= \(\frac{58.5}{38.75}\) = 1.50

Question 14.
What are the necessary conditions for an ideal solution? Give two examples. For an ideal solution
1. There is no change in volume on mixing two components (solute and solvent)
∆Vmixing = O

2. There is no exchange of heat when the solute is dissolved in solvent (∆Hmixing = 0)

3. Escaping tendency of the solute and the solvent present in it should be the same as in pure liquids.

4. Examples – For ideal solution: Benzene and toluene, n-Hexane and n-Heptane, ethyl bromide and ethyl iodide, chlorobenzene and bromobenzene.

Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions

Question 15.
Explain how non-ideal solutions show positive deviation from Raoult’s law.
Answer:

  1. Let us consider the positive deviation shown by a solution of ethyl alcohol and water.
  2. In this solution, the hydrogen bonding interaction between ethanol and water is weaker than those hydrogen bonding interactions amongst themselves (ethyl alcohol-ethyl alcohol and water-water interaction).
  3. This results in the increased evaporation of both components from the aqueous solution of ethanol.
  4. Consequently, the vapour pressure of the solution is greater than the vapour pressure predicted by Raoult’s law.
  5. Here, the mixing OCCSS is endothermic i.e., (∆Hmixing > O) and there will be a slight increase in volume (∆Vmixing > O)

Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-80

Question 16.
Explain with suitable example about negative deviation from law.
Answer:
1. Let us consider a solution of phenol and aniline. Both phenol and aniline form hydrogen-bonding interactions amongst themselves.

2. When mixed with aniline, the phenol molecule forms hydrogen bonding interactions with aniline, which are Stronger than the hydrogen bonds formed amongst themselves.

3. Formation of new hydrogen bonds considerably reduces the escaping tendency of phenol and aniline from the solution.

4. Asa result, the vapour pressure of the solution is less and there is a slight decrease in volume (∆Vmixing < 0) on mixing.

5. During this process evolution of heat takes place i.e., ∆Vmixing < 0 (exothermic).

6. Examples – Acetone + Chloroform, Chloroform + Diethyl ether
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-81

Question 17.
The vapour pressure of a solution containing a nonvolatile, non-electrolyte solute is always lower than that of pure solvent. Give reason.
Answer:
1. The vapour pressure of a solution (P) containing a full volatile solute is lower than that of pure solvent (P°).

2. Consider a closed system is which a pure solvent is in equilibrium with its vapour. At equilibrium the molar Gibbs free energies of solvent in a liquid and gaseous phase are equal (∆G = O).

3. When a solute is added to this solvent the dissolution takes place and its free energy (G) decreases due to increase in entropy.

4. In order to maintain the equilibrium, the free energy of the vapour phase must also decrease.

5. At a given temperature, the only way to lower the free energy of the vapour is to reduce its pressure.

6. Thus the vapour pressure of the solution must decrease to maintain the equilibrium.

Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions

Question 18.
Show that relative lowering of vapour pressure is a colligative property.
Answer:
According to Raoult’s law,
Psolution xA, where xA = mole fraction of solvent.
Psolution = k . xA, where k = proportionality constant
For a pure solvent,
Vapour pressure = P°, xA = 1
solution = k x 1 = k
Substituting P°solvent in Raoult’s law
Psolution = P°solvent . xA
Relative lowenng of vapour pressure
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-82
substituting Psolution as P°xB in the above eaquation
Relative lowering of vapour pressure
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-83
xA + xB = I
where xB = mole fraction of solute. It is clear that the relative lowering of vapour pressure depends only on the mole fraction ofthe solute (xB) and is independent of its nature. Therefore relative lowering of vapour pressure is a colligative property.

Question 19.
Explain why boiling point of solution is greater than that of pure solvent?
Answer:
When a non volatile solute is added to a pure solvent at its boiling point, the vapour pressure of the solution is lowered below 1 atm. To bring the vapour pressure again to I atm the temperature of the solution has to be increased.

As a result, the solution boils at a higher temperature (Tb) than the boiling point of the pure solvent (T°b). This increase in the boiling point is known as elevation of boiling point ∆Tb = Tb – T°b.

Question 20.
Graphically prove that Tb ¡s greater than T°b.
Answer:
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-84
1. The vapour pressure of the solution increases with increase in temperature. The variation of vapour pressure with respect to temperature of pure water is given by the curve – A.

2. At 100°C, the vapour pressure of water is equal to I atm. Hence, the boiling point of water is 100°C (T°b).

3. When a solute is added to water, the vapour pressure of the resultant solution is lowered. The variation of vapour pressure with respect to temperature for the solution is given by curve-B.

4. From the graph, it is evident that the vapour pressure of the solution is equal to 1 atm. pressure at the temperature Tb which is greater than T°b. The difference between these two temperatures (Tb – T°b) gives the elevation of boiling point.
∆Tb = Tbb.

Question 21.
Derive the relationship between the elevation of boiling point and molar mass of non volatile solute.
Answer:
The elevation of boiling point ∆Tb = Tbb.
∆Tb is directly proportional to the concentration of the solute particles.
∆Tb ∝ m, (m = molaLiiy)
∆Tb = kb. m, where kb = ebullioscopic constant
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-85

Question 22.
Define

  1. freezing point
  2. Depression in freezing point.

Explain with graph.
Answer:
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-86
1. Freezing point is defined as the temperature at which the solid and the liquid states of the substances have the same vapour pressure.

2. When a non volatile solute is added to water at its freezing point, the freezing point of water is lowered from 0°C. The lowering of freezing point of the solvent when a solute is added is called depression in freezing point AT1..

3. ∆Tf = T0f – Tf

Question 23.
Define

  1. cryoscopic constant
  2. ebullioscopic constant

Answer:

1. ∆Tf = kf. m, where kf = cryoscopic constant. If m = 1. then ATf = kf
kf is defined as depression in freezing point for 1 molal solution.

2. ∆Tf = kf. m where kf ebullioscopic constant. If m = 1 then ATf = kf
kb is defined as elevation in boiling point for 1 molal solution.

Question 24.
What are the significances of osmotic pressure over other colligative properties ?
Answer:
1. Unlike elevation of boiling point and the depression in freezing point, the magnitude of osmotic pressure is large.

2. The osmotic pressure can be measured at room temperature enables to determine the molecular mass of biomolecules which are unstable at higher temperature.

3. Even for a very dilute solution, the osmotic pressure is large.

Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions

Question 25.
What is haemolysis ? intravenous fluid are isotonic to blood?
Answer:
1. The osmotic pressure of the blood cells is approximately equal to 7 atm at 37°C.

2. The intravenous injections should have saine osmotic pressure as that of the blood (isotonic vith blood).

3. If the intravenous solutions are too dilute that is hypotonie, the solvent from outside of the cells flow into the cell to normalise the osmotic pressure and this process is called haernolysis causes the cells to burst.

4. On the other hand, if the solution is too concentrated, that is hypertonic. the solvent molecules will flow out of the cells,which causes the cells to shrink and die.

5. For this reason, the intravenous fluids are prepared such that they are isotonic to blood (0.9% mass/volume sodium chloride solution).

Question 26.
Explain reverse osmosis.
Answer:
1. The pure water moves through the semipermeable membrane to the NaCl solution due to osmosis.

2. This process can be reversed by applying pressure greater than the osmotic pressure to the solution side. Now the pure water moves from the solution side to the solvent side and this process is called reverse osmosis.

3. Reverse osmosis can be defined as a process in which a solvent passes through a semipermeable membrane in the opposite direction of osmosis, when subjected to a hydrostatic pressure greater than the osmotic pressure.

Question 27.
Explain about the application of reverse osmosis in water purification.
Answer:
1. Reverse osmosis is used in the desalination of sea water and also in the purification of drinking water.

2. When a pressure higher than the osmotic pressure is applied on the solution side (sea water) the water molecules moves from solution side to the solvent side through semi permeable membrane (opposite to osmotic flow). The pure water can be collected.

3. Cellulose acetate (or) polyamide membranes are commonly used in commercial system.
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-87

Question 28.
Acetic acid is found to have molar mass as 120 g mol-1. Prove it.
Answer:
1. In certain solvent, solute molecules associate to form a dimer. This reduces the total number of molecules formed in solution and as a result the calculated molar mass will be higher than the actual molar mass.

2. Acetic acid in benzene exist as a dimer
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-88

3. The molar mass of acetic acid calculate using colligative properties is found to be around 120 g mol-1 is two times of the actual molar mass 60 g mol-1.

Question 29.
Depression in freezing point of NaCI is twice that of in urea. Why?
Answer:
1. The electrolyte NaCI dissociates completely into its constituent ions in their aqueous solution. This causes an increase in the total number olparticles present in the solution.

2. When we dissolve 1 mole of NaCI in water it. dissociates and gives 1 mole of Na+ and 1 mole of Cl. Hence the solution will have 2 moles of particles.

But when we dissolve 1 mole of urea (non electrolyte) in water it appears as 1 mole only. So the colligative property value would be double in NaCl than in urea.

Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions

Question 30.
What is van’t Hoff factor? Calculate the van’t Hoff factor value for

  1. acetic acid
  2. NaCl

Answer:
1. van’t Hoff factor is defined as the ratio ofthe actual molar mass to the abnormal (calculated) molar mass of the solute.

2.
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-89
van’t Hoff factor (1) for acetic acid = \(\frac { 60 }{ 120 }\) = 0.5

3. van’t Hoff factor (2) for NaCl = \(\frac { 117 }{ 58.5 }\) = 2

Question 31.
Differentiate between ideal solution and non-ideal solution.
Answer:
Ideal solution
An ideal solution is a solution in which each component obeys the Raoult’s law over the entire range of concentration.
For an ideal solution,

  • ∆Hmixing = 0
  • ∆Vmixing = 0

Example: Benzenc and toluene n – Hexane and n – Heptane

Non-ideal solution
The solutions which do not obey Raoult’slaw over the entire range of concentrationsare called non-ideal solution.
For a non-ideal solution.

  • ∆Hmixing \(\quad \neq\) 0
  • ∆Vmixing \(\quad \neq\) 0

Example: Ethyl alcohol and Cyclohexane, Benzene and acetone.

Question 32.
Explain the factors when i = 1, i < 1 and i >1 ?
Answer:
1. For a solute that does not dissociate or associate the vant’s hoff factor is equal to 1 (i = 1) and the molar mass will be close to the actual molar mass.

2. For that solute that associate to form higher oligomers in solution, the van’t Hoff factor will be less than 1 (i < 1) and the observed molar mass will be greater than the actual molar mass.

3. For solutes that dissociates into their constituent ions the van’t Hoff factor will be more than one (i > 1) and the observed molar mass will be less than the normal molar mass.

Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions

Question 33.
State Henry’s law and mention some of its important applications.
Answer:
Henry’s law: The solubility of a gas in a liquid is directly proportional to the pressure of the gas.
Application of Henry’s law:

  1. In the production of carbonated beverages
    (as solubility of CO2 increase at high pressure).
  2. In the deep sea diving.
  3. In the function of lungs.
  4. For climbers or people living at high altitudes,

Question 34.
What type of non – idealities are exhibited by cyclohexane – ethanol and acetone – chloroform mixture? Give reason for your answer.
Answer:
Ideal solutions are those which obey Raoult’s law over extreme range of concentration. Ideal solutions have another important properties:

  • ∆Hmix = 0
  • ∆Vmix = 0

Here-forces of attraction between A – A. B – B and A – B are of the same order. Non ideal solutions do not obey Raoult’s law over the entire range of concentration.
∆Hmixing\(\quad \neq\) 0 and ∆Vmixing\(\quad \neq\) 0

Cyclohexane – ethanol mixture shows positive deviation from Raoult’s law because forces of attraction between cyclohexane and ethanol are less than in between pure cyclohexane as well as pure ethanol.

Acetone-Chloroform mixture shows negative deviation from Raoults law because forces of attraction between acetone and chloroform are higher than that in between pure acetone and pure chloroform molecules.

Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions

Question 35.
Given below is the sketch of a plant for carrying out a process.
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-90

  1. Name the process occurring in the above plant.
  2. To which container does the net flow of solvent take place?
  3. Name one SPM which can he used in this plant.
  4. Give one practical use of the plant.

Answer:

  1. Reverse osmosis
  2. In fresh water container from salt water container.
  3. Cellulose acetate is semipermeable membrane (SPM)
  4. Purification of water

Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions

Question 36.
Define the term osmotic pressure. Describe how the molecular mass of a substance can be determined by a method based on measurement of osmotic pressure?
Answer:
π = CRT
π = \(\frac { n }{ V }\)RT
πV = nRT
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-91
Osmotic pressure is inversely proportional to the molecular mass of the soLute.

Question 37.
1. Menthol is a crystalline substance with peppermint taste. A 6.2% solution of menthol in cyclohexane freezes at – 1.95°C.

Determine the formula mass of menthol. The freezing point and molal depression constant of cyclohexane are 6.5°C and 20.2 K m-1, respectively.

2. State Henry’s Law and mention its two important applications.

3. Which of the following has higher boiling point and why? 0.1 M NaCl or 0.1 M Glucose
Answer:
1.
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-92
MB = 158 g mol-1

2. Henry’s Law:
The solubility of a gas in a liquid is directly proportional to the pressure of the gas.
Applications:

  • Solubility of CO2 is increased at high pressure.
  • Mixture of He and O2 are used by deep sea divers because he is less soluble than nitrogen.

3. 0.1 M NaCI, because it dissociates in solution and furnishes greater number of particles per unit volume while glucose being a non-electrolyte does not dissociate.

Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions

Question 38.
Water is a universal solvent. But alcohol also dissolves most of the substances soluble in water and also many more. Boiling point of water is 100°C and that of alcohol is 80°C. The specific heat of water is much higher than the specific heat of alcohol.

  1. List out three possible differences if instead of water as the liquid ¡n our body we had alcohol.
  2. What value can you derive from this special property of water and its innumerable uses in sustaining life on earth?

Answer:
1.
(i) Even a small rise in temperature in the surroundings will raise the temperature of’ the body because the specific heat of alcoholis much less than the specific heat of water. So, in order to cool the body, more sweating will take place.

(ii) As there is less H bonding in alcohol, it will gel evaporated faster. The alcohol will be evaporated at such a faster rate that the liquid has to be ingested all the time.

(iii) Ice which floats on water helps aquatic life to exist even in winter as water insulates the heat from liquid below it to go back to the surroundings. Solid alcohol does not have such special properties.

2. Praise is to the almighty that has so thoughtfully given such special properties to water and made it a liquid that could sustain life on earth.

Question 39.
State Henry’s law for solubility of a gas in a liquid. Explain the significance of Henry’s law constant (KH). At the same temperature, hydrogen is more soluble in water than helium. Which of theni will have a higher value of KH and Why?
Answer:
Henry’s law states that the solubility of a gas in liquid at a given temperature is directly proportional to the partial pressure of the gas.
P = KH x
where P is the pressure of the gas, x is the mole fraction of the gas in the solution and KH is the Henry’s law constant. KH is a function of the nature oIgas.

Higher the value of KH at a given temperature. lower is the solubility of the gas in the liquid. As helium is less soluble in water, so it has a higher value of KH than hydrogen.

Henry’s Law:
As dissolution of agar in liquid is an exothermic process, therefore, the solubility should decrease with in increase in temperature.

Question 40.
What is meant by positive and negative deviations from Raoult’s law and how is the sign ∆Hmix of related to positive and negative deviations from Raoult’s law?
Answer:
Negative deviations:
In these type of deviations, the partial vapour pressure of each component A and B of solution is higher than the vapour pressure calculated from Raoult’s law. For example -Water and ethanol, chloroform and water.

Positive deviations:
In case of positive deviation A – B interactions are weaker than those between A – A or B – B. This means that in such solutions molecules or A (or B) will find it easier to positive deviation from Raoult’s law.

Samacheer Kalvi 11th Chemistry Solutions 5 Marks Questions and Answers

II. Answer the following questions in detail:

Question 1.

  1. Define solution.
  2. Explain the types of solutions with suitable example.

Answer:
1. A solution is a homogeneous mixture of two or more substances, consisting of atoms. ions or molecules.

2. Types and examples of solution.
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-93

Question 2.

  1. Define Solubility
  2. Explain the factors that influences the solubility

Answer:

1. The solubility of a substance at a given temperature is defined as the amount of the solute that can be dissolved in 100 g of the solvent at a given temperature to form a saturated solution.

2. Factors influencing solubility
(a) Nature of solute and solvent: Sodium chloride, an ionic compound readily dissolves in polar solvent such as water but it does not dissolve in non polar solvent such as benzene. Most of the organic compounds dissolve in organic solvent and do not dissolve in water.

(b) Effect of temperature: Generally, the solubility of a solid solute in a liquid solvent increases with increase in temperature. The dissolution of NaCl does not vary as the maximum solubility is achieved at normal temperature.

The dissolution of ammonium nitrate is endothermic, the solubility increases with increase in temperature. The dissolution of eerie sulphate is exothermic and the solubility decreases with increase of temperature. In the case of gaseous solute in liquid solvent the soluhility decreases with increase in temperature.

Effect of pressure:
Generally the change in pressure does not have any significant effect in the solubility of solids and l?quids as they are not compressible. However, the solubility of gases generally increases with increase of pressure.

Question 3.
Explain about the factors that are responsible for deviation from Raoult’s law.
Answer:
1. Solute-solvent interactions:
For an ideal solution, the interaction between the solvent molecules (A – A), the solute molecules (B – B) and between the solvent and solute molecules (A – B) are expected to be similar. if these interactions are dissimilar, there will be a deviation from ideal behaviour.

2. Dissolution of solute:
When a solute present in a solution dissociates to give its constituent ions, the resultant ions interact strongly with the solvent and causes deviation from Raoult’s law. e.g., KCI in water deviates from ideal behaviour due to dissociation as K+ and Cl ion which form strong ion-dipole interaction with water molecules.

3. Association of solute:
Association of solute molecules can also cause deviation from ideal behaviour. For example in solution acetic acid exists as a dimer by forming intermolecular hydrogen bonds and hence deviates from Raoult’s law.

4. Temperature:
An increase in temperature of the solution increases the average kinetic energy of the molecules present in the solution which cause decrease in the attractive force between them. As result, the solution deviates from Raoult’s law.

5. Pressure:
At high pressure, the molecules tends to stay close to each other and therefore there will be an increase in their intermolecular attraction. Thus a solution deviates from Raoult’s law at high pressure.

6. Concentration:
When the concentration is increased by adding solute, the solvent-solute interaction becomes significant. This causes deviation from Raoult’s law.

Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions

Question 4.
How would you determine molar mass from relative lowering of vapour pressure.
Answer:
1. The measurement of relative lowering of vapour pressure can be used to determine the molar mass of a non-volatile solute.

2. A known mass of the solute is dissolved in a known quantity of solvent. The relative lowering of vapour pressure is measured experimentally.

3. According to Raoult’s law, the relative lowering of vapour pressure is
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-94
WA = weight of solvent
WB = weight of solute
MA = Molar mass of solvent
MB = molar mass of solute
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-95
where nA = number of moles of solvent
nB = number of moles of solute.
For dilute solution, nA > > nB, nA + nB = nA
Then, Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-96
Number of moles of solvent and solute arc
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-97
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-98
From the above equation, molar mass of the solute MB can be calculated using the known values of WA, WB, MA and the measured relative lowering of vapour pressure.

Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions

Question 5.
How would you determine the molar mass from osmotic pressure.
Answer:
According to van’t Hoff equation
π = CRT
C = \(\frac { n }{ V }\)
Here n = number of moles of solute dissolved in ‘V’ litre of the solution.
π = \(\frac { n }{ V }\) . RT = πV = nRT
If the solution is prepared by dissolving WB of the non-volatile solute in WA g of solvent, then the number of moles of ‘n’ is
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-99
where
MB = molar mass of the solute
Substituting n value, we get
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-100
From the above equation, we can calculate the molar mass of the solute.

Question 6.
What are ideal and non-ideal solutions? Explain with suitable diagram the behaviour of ideal solutions.
Answer:
Ideal solutions:
The solutions which obey Raoult’s law over the entire range of concentration are known as ideal solutions. Ideal solutions are formed by mixing the two components which are identical in molecular size, in structure and have almost identical intermolecular forces.

Examples:

  1. Benzene and toluene
  2. n – Hexane and n-Heptane
  3. Chiorobenzene and bromobenzene.

Characteristics:

  1. They must obey Raoult’s law.
  2. ∆H mixing should be zero.
  3. ∆W mixing should be zero, i.e. volume change on mixing is zero.

Non – ideal solutions:
The solutions which do not obey Raoult’s law are called non-ideal solutions. In case of non – ideal solutions there is a change in volume and heat energy when the two components are mixed.
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-101

Characteristics:

  1. They does not obey Raoult’s law.
  2. ∆Vmix \(\quad \neq\) 0
  3. ∆Hmix \(\quad \neq\) 0

Behaviour of Ideal Solutions:
A plot of P1 or P2 versus the mole fraction x1 and x2 for an ideal solution gives a linear plot. These Lines (I and II)pass through the points and respectively whenx1 and x2 is equal to unity.

Similarly the plot (Line III) of Ptotal versus x2 is also linear. The minimum value of is P1° and the maximum value is P2°, assuming that component 1 is less volatile than component 2, i.e. P1° < P20.

Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions

Question 7.
Explain with a suitable diagram and appropriate example, why some non-ideal solution shows positive deviation from Raou It’s law.
Answer:
Some non-ideal solutions show positive deviation from Raoult’s law. Consider a solution of two components A and B.  If A-B interactions in the solution are weaker than the A – A and B – B interactions in the two liquids forming the solution, then the escaping tendency of molecules A and B from the solution become more than in pure liquids.

The total vapour pressure will be greater than the corresponding vapour pressure as expected on the basis of Raoult’s law. This type of behaviour of solution is called positive deviation from Raoult’s law. The boiling point of such solutions are lowered. Mathematically,
PA < PA0 xA
PB < PB0 xB
The total vapour pressure is less than PA + PB
P < PA + PB
P < P°A x xA + P°B xB
Hence
P1 = PA
P2 = PB
Examples of solutions showing positive deviations

  1. Ethyl alcohol and water
  2. Benzene and acetone
  3. Ethyl alcohol and cyclohcxanc
  4. Carbon tetrachloride and chloroform.

Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-102

Question 8.

  1. What is Osmotic pressure and how is it related to the molecular mass of a non volatile substances?
  2. What advantage the osmotic pressure method has over the elevation of boiling point method for determining the molecular mass?

Answer:
1. Osmotic pressure:
It is the pressure of the solution column that can prevent the entry of solvent molecules through a semi-permeable membrane, when the solution and the solvent are separated by the same. It is denoted by π. Its unit is mm 11g or atmosphere.
We know that, π = CRT
where π is the osmotic pressure and R is the gas constant
π = \(\frac { { n }_{ 2 } }{ V }\) RT
where V is volume of solution per litre containing n2 moles of solute.
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-103
By the above relation molar mass of solute can be calculated.

2. The osmotic pressure method has the advantage over other methods as pressure measurement is around the room temperature and molarity of the solution is used instead of molality.

The technique of osmotic pressure for determination of molar mass of solutes is particularly useful for biomolecules as they are generally not stable at higher temperature and polymers have poor solubility.

III. Numerical Problems

Question 1.
Calculate the mole fraction of benzene ¡n solution containing 30% by mass in carbon tetrachioride.
Solution:
30% of benzene in carbon tetrachloride by mass means that Mass of benzene in the solution = 30g
Mass of solution = 100g
Mass of carbon tetrachloride = 100g – 30g = 70g
Molar mass of benzene (C6H6) = 78 g mol-1
Molar mass of CCl4 = 12 + (4 x 35.5) 154g mol-1
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-104

Question 2.
Calculate (he molarity of each of the following solutions:
Solution:

  1. 30 g of CO(NO3)2. 6H2O = in 4.3 L of solution
  2. 30 mL of 0.5 M H2SO4 diluted to 500 mL.

1. Molar mass of CO(NO3)2. 6H2O = 58.7 + 2(14 + 48) + (6 x 8)g mol-1
= 58.7 + 124 + 108g mol-1 = 290.7 gmol-1
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-105
Volume of solution = 4.3 L
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-106

2. 1000 mL of 0.5 M H2SO4 Contain H2SO4 = 0.5 moles
30 mL of 0.5 M H2SO4 contain H2SO4 = \(\frac { 0.5 }{ 1000 }\) x 30 mole = 0.015 mole
Volume of solution = 500 mL = 0.500 L
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-107

Question 3.
Calculate the mass of urea (NH2CONH2) required in making 2.5 kg of 0.25 molal aqueous solution.
Solution:
0.25 molal aqueous solution means that
Moles of urea = 0.25 mole
Mass of solvent (water) = 1 kg = 1000 g
Molar mass of urea = 14 + 2 + 12 + 16 + 14 + 2 = 6Og mol-1
0.25 mole of urea = 60 x 0.25 mole = 15 g
Total mass of the solution = 1000 + 15 g = 1015 g = 1.015 g
Thus, 1.015 kg of solution contain urea = 15 g
2.5 kg of solution will require urea = \(\frac { 15 }{ 1.015 }\) x 2.5 kg = 37g

Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions

Question 4.
H2S, a toxic gas with rotten egg like smell is used for the qualitative analysis. 1f the solubility of H2S in water at STP is 0.195 m. Calculate Henrvs law constant.
Solution:
Solubility of H2S gas = 0.195 m
= 0.195 mole in 1 kg of the Solvent (water)
1 kg of the solvent (water) = 1000 g Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-108
Mole fraction of H2S gas in the solution (x) = \(\frac { 0.195 }{ 0.195 + 55.55 }\) = 0.0035
Pressure at STP = 0.98 7 bar
Applying Henry’s law
PH2S = KH x xH2S
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-109

Question 5.
Vapour pressure of pure water at 298 K is 23.8 mm Hg. 50 g of urea (NH2CONH2) is dissolved in 850 g of water. Calculate the vapour pressure of water for this solution and its relative lowering.
Solution:
Here
1 = 23.8 mm
W2 = 50g
M2 (urea) = 60g mol-1
W1 = 850g
M1(Water) = 18g mol-1
Here we have to calculate Ps
Applying Raoult’s law,
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-110
Thus, relative lowering of vapour pressure = 0.017
Substituting P° = 23.8 mm Hg
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-111
We get,
23.8 – Ps = 0.017 Ps
Ps = 23.4 mm Hg
Thus, vapour pressure of water in the solution = 23.4 mm Hg

Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions

Question 6.
Boiling point of water at 750 mm Hg is 99.63°C. How much sucrose is to be added to 500g of water such that it boils at 100°C? .
Solution:
Elevation in boiling point required, ∆Tb = 100 – 99.63° = 0.37°
Mass of solvent (water) W1 = 500g
Mass of solute, C12H22O11 = 342 g mol-1
Molar mass of solvent M1 = 18 g mol-1
Applying the formula,
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-112

Question 7.
Concentrated nitric acid used in laboratory work is 68% nitric acid by mass in aqueous solution. What should be the molarity of such a sample of the acid if the density of the solution is 1.504g mL-1?
Solution:
68% nitric acid by mass means that
Mass of nitric acid = 68 g
Mass of solution = 100 g
Molar mass of HNO3 = 63g mol-1
68g HNO3 = mole = 1.079 mole
Density of solution = 1.504 g mL-1
Volume of solution = \(\frac { 100 }{ 1.504 }\) mL = 66.5 mL = 0.0665 L
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-113

Question 8.
A solution is obtained by mixing 300 g of 25% solution and 400 g of 40% solution by mass. Calculate tile mass percentage of the resulting solution.
Solution:
300 g of 25% solution contains solute = 75g
400g of 40% solution contains solute = 160 g
Total mass of solute = 160 + 75 = 235 g
Total mass oÍ’ solution = 300 + 400 = 700 g
% of solute in the final solution = \(\frac { 235 }{ 700 }\) x 1oo = 33.5%
% of water in the finaI solution = 100 – 33.5 = 66.5%

Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions

Question 9.
A sample of drinking water was found to be severely contaminated with chloroform (CHCI3) supposed to be a carcinogen. The level of contamination was 15 ppm (by mass)

  1. express this in percentage by mass
  2. determine the molality of chloroform in the water sample.

Solution:
1. 15 ppm means 15 parts in million (106) parts by mass in the solution
% of mass = \(\frac { 15 }{ { 10 }^{ 6 } }\) x 100 = 1.5 x 10-4

2. Taking 15g chloroform in 106g of the solution
Mass of the solvent = 106 g
Molar mass of CHCl3 = 12 + 1 + (3 x 35.5) = 119.5 g mol-1
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-114

Question 10.
An aqueous solution of 2% non-volatile solute exerts a pressure of 1.004 bar at normal boiling point of the solvent. What is the molar mass of the solute?
Solution:
Vapour pressure of pure water at the boiling point
(P°) = 1 atm 1.013 bar
Vapour pressure of solution Ps = 1.004 bar
M1 = 18 g mol-1
M2 = ?
Mass of solute = W2 = 2g
Mass of solution = 100g
Mass of solvent W1 = 98 g
Applying Raoult’s law for dilute solution
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-115

Question 11.
A 5% solution (by mass) of cane sugar in water has freezing point of 271 K. Calculate the freezing point of 5% glucose in water if freezing point of pure water is 273.15K.
Solution:
Molar mass of cane sugar
C12H22O11 = 342 g mol-1
Molality of sugar = \(\frac { 5 x 1000 }{ 342 x 100 }\) = 0.146
∆T2 for sugar solution = 273.15 – 271 = 2.15°
∆Tf = Kf x m
Kf = \(\frac { 2.15 }{ 0.146 }\)
Molality of glucose solution = \(\frac { 5 }{ 180 }\) x \(\frac { 1000 }{ 100 }\) = 0.278 m
∆Tf (Glucose) = \(\frac { 2.15 }{ 0.146 }\) x 0.278 = 4.09°K
Freezing point of glucose solution = 273.15 – 4.09 = 269.06 K

Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions

Question 12.
Calculate the amount of benzoic acid (C6HCOOH) required for preparing 250 mL of 0.15 M solution in methanol.
Solution:
0.15 M solution means that 0.15 moles of C6H5COOH is present in IL
= 1000 mL of the solution
Molar mass of C6H5COOH = 72 + 5 + 12 + 32 + 1 = 122 g mol-1
Thus, 1000 mL of solution contains benzoic acid = 18.3g
250 mL of solution will contain benzoic acid
= \(\frac { 18.3 }{ 1000 }\) x 250 = 4.575 g

Question 13.
A solution containing 8 g of a substance in 100 g of diethyl ether boils at 36.86°C, whereas pure ether boils at 35.60 °C. Determine the molecular mass of the solute (For ether Kb 2.02 K kg mol-1)
Solution:
We have, mass of solute, W2 = 8 g
Mass of solvent, W1 = 100 g
Elevation of boiling point
∆Tb = 36.86 – 35.60 = 1.260C
Kb = 2.02
Molecular mass of the solute
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-116
= 128.25g mol-1

Question 14.
Ethylene glycol (molar mass = 62 g mol-1) is a common automobile antifreeze. Calculate the freezing point of a solution containing 12.4 of this substance in 100 g of water. Would it be advisable to keep this substance ¡n the car radiator during summer? (Kf for water = 1.86 k kg/mol-1) (Kb for water = 0.512 K kg/mol-1)
Solution:
Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-117
Since water boils at 100°C, so a solution containing ethylene glycol will boil at 101.024 °C, SO it is advisable to keep this substance in car radiator during summer.

Question 15.
15.0 g of an unknown molecular material is dissolved in 450g of water. The resulting solution freezes at – 0.34°C. What is the molar mass of the material? Kf for water = 1.86 K kg mol-1.
Solution:
W(solute) = 1 5.0 g
W(solvent) = 450 g
∆Tf = T°f – Tf = 0 – ( – 0.34) = 0.34 °C
∆Tf = kf m
0.34 = 1.86 x \(\frac { 15 }{ M }\) x \(\frac { 1000 }{ 450 }\)
M = \(\frac { 1.86 x 15 x 1000 }{ 0.34 x 450 }\) = 182.35 g mol-1

Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions

Common Errors
Common Errors:

  1. Students are writing solute, solvent, students get confused to write A (or) B, 1 (or)2.
  2. Mole, mole fraction may be confused.
  3. In writing osmosis definition Students get confused in mentioning concentration terms.
  4. van’t Hoff factor I formula may be con fused.
  5. Students may get contused rhen they write solute and solvent.
  6. Mole and mole fraction may be confused by students.
  7. Standard solutions must be known.
  8. When students write Raoult’s law, they get confused with solute and solvent.
  9. When they write the definition of osmosis, the conc. term may be little con fused.
  10. van’t Hoff equation may be written wrongly.

Rectifications:

  1. Always solvent is first so it is denoted as A (or) 1 solute is second so, it is denoted as B (or)2.
  2. Mole = n ; Mole fraction x
  3. Osmosis-movenient of solvent from low concentration to high concentration through a semipermeable membrane.
  4. Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-118
  5. For e.g.. solid in liquid means solid is the solute and liquid is the solvent.
  6. Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-119
  7. 1 N = 1 normal solution, 0.1 N Decinormal solution, 0.01 N = Centinormal solution
  8. In Raoult’s law, “A” is always solvent and “B” is always solute.
  9. In osmosis, always solvent rnoes through semi permeable membrane from low concentration to high concentration.
  10. van’t Hoff factory = i
    Samacheer Kalvi 11th Chemistry Solutions Chapter 9 Solutions-120

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Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Students can Download Chemistry Chapter 1 Basic Concepts of Chemistry and Chemical Calculations Questions and Answers, Notes Pdf, Samacheer Kalvi 11th Chemistry Solutions Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Samacheer Kalvi 11th Chemistry Chapter 1 Basic Concepts of Chemistry and Chemical Calculations Textual Evaluation Solved

I. Choose the Best Answer

Question 1.
40 ml of methane is completely burnt using 80 ml of oxygen at room temperature. The volume of gas left after cooling to room temperature is ………..
(a) 40 ml CO2 gas
(b) 40 ml CO2 gas and 80 ml H2O gas
(c) 60 ml CO2 gas and 60 ml H2O gas
(d) 120 ml CO2 gas
Answer:
(a) 40 ml CO2 gas
Solution:
CH4(g)  + 2O2(g)  CO2(g) + 2 H2O(l)

Content CH4 O2 CO2
Stoichiometric coefficient 1 2 1
Volume of reactants allowed to react 40 mL 80 mL          –
Volume of reactant reacted and product formed 40 mL 80 mL 40 mL
Volume of gas after cooling to the room temperature

Since the product was cooled to room temperature, water exists mostly as liquid. Hence, option (a) is correct

Question 2.
An element X has the following isotopic composition 200X = 90 %, 199X = 8 % and 202X = 2 %. The weighted average atomic mass of the element X is closest to …………
(a) 201 u
(b) 202 u
(c) 199 u
(d) 200 u
Answer:
(d) 200 u
= \(\frac {(200 × 90) + (199 × 8) + (202 × 2) }{100}\) = 199.96 = 200 u

Question 3.
Assertion:
Two moles of glucose contain 12.044 × 1023 molecules of glucose.

Reason:
The total number of entities present in one mole of any substance is equal to 6.02 × 1022
(a) both assertion and reason are true and the reason is the correct explanation of the assertion
(b) both assertion and reason are true but the reason is not the correct explanation of the assertion
(c) the assertion is true but the reason is false
(d) both assertion and reason are false
Answer:
(c) the assertion is true but the reason is false

Correct reason:
The total number of entities present in one mole of any substance is equal to 6.022 x 1023

Question 4.
Carbon forms two oxides, namely carbon monoxide and carbon dioxide. The equivalent mass of which element remains constant?
(a) Carbon
(b) Oxygen
(c) Both carbon and oxygen
(d) Neither carbon nor oxygen
Answer:
(b) Oxygen

Reaction 1:
2 C + O2 → 2 CO2
2 × 12 g carbon combines with 32 g of oxygen.
Hence, Equivalent mass of carbon = \(\frac {2 × 12}{32}\) × 8 = 6

Reaction 2:
C + O2 → 2 CO2
12 g carbon combines with 32 g of oxygen.
Hence, Equivalent mass of carbon = \(\frac {12}{32}\) × 8 = 3

Question 5.
The equivalent mass of a trivalent metal element is 9 g eq-1 the molar mass of its anhydrous oxide is ………..
(a) 102 g
(b) 27 g
(c) 270 g
(d) 78 g
Answer:
(a) 102 g
Let the trivalent metal be M3+
Equivalent mass = mass of the metal / valance factor
9g eq-1 = mass of the metal / 3 eq
Mass of the metal = 27 g
Oxide formed M2O3
Mass of the oxide = (2 × 27) + (3 × 16) = 102 g

Question 6.
The number of water molecules in a drop of water weighing 0.018 g is ………….
(a) 6.022 × 1026
(b) 6.022 × 1023
(c) 6.022 × 1020
(d) 99 × 1022
Answer:
(c) 6.022 × 1020
Weight of the water drop = 0.0 18 g
No. of moles of water in the drop = Mass of water / molar mass = 0.018/18 = 10-3 mole
No of water molecules present in I mole of water = 6.022 × 1023
No. water molecules in one drop of water (10 moles) = 6.022 × 1023 × 10-3 = 6.022 × 1020

Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Question 7.
1 g of an impure sample of magnesium carbonate (containing no thermally decomposable impurities) on complete thermal decomposition gave 0.44 g of carbon dioxide gas. The percentage of impurity in the sample is ………..
(a) 0 %
(b) 4.4 %
(c) 16 %
(d) 8.4 %
Answer:
(c) 16%
Mg CO3 → MgO + CO2
Mg CO3 : (1 × 24) + (1 × 12) + (3 × 16) = 84 g
CO2 : (1 × 12) + (2 × 16) 44g
100% pure 84 g MgCO3 on heating gives 44 g CO2
Given that I g of MgCO3 on heating gives 0.44 g CO2
Therefore, 84 g MgCO3 sample on heating gives 36.96 g CO2 = 100%
Percentage of purity of the sample = \(\frac{100 \%}{44 \mathrm{g} \mathrm{CO}_{2}}\) × 36.96 g CO2 = 84%
Percentage of impurity = 16%

Question 8.
When 6.3 g of sodium bicarbonate is added to 30 g of the acetic acid solution, the residual solution is found to weigh 33 g. The number of moles of carbon dioxide released in the reaction is-
(a) 3
(b) 0.75
(c) 0.075
(a) 0.3
Answer:
(c) 0.075
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
The amount of CO2 released, x = 3.3 g
No. of moles of CO2 released = 3.3 / 44 = 0.075 mol

Question 9.
When 22.4 liters of H2 (g) is mixed with 11.2 liters of Cl2 (g), each at 273 K at 1 atm the moles of HCl (g), formed is equal to ………..
(a) 2 moles of HCl (g)
(b) 0.5 moles of HCl (g)
(c) 1.5 moles of HCl (g)
(d) 1 moles of HCl (g)
Answer:
(d) 1 moles of HCl (g)
Solution:
H2(g) + Cl2(g) → 2 HCl (g)

Content H2(g) cl2(g) HCl (g)
Stoichiometric coefficient 1 1 2
No. of moles of reactants allowed to react at 273 K and 1 atm pressure 22.4 L (1 mol) 11.2 L (0.5 mol)
No. of moles of a reactant reacted and product formed 0.5 0.5 1
Amount of HCl formed 1 mol

Question 10.
Hot concentrated sulfuric acid is a moderately strong oxidizing agent. Which of the following reactions does not show oxidizing behavior?
(a) Cu + 2H2SO4 → CuSO4 + SO2 + 2H2O
(b) C + 2H2SO4 → 4 CO2 + 2SO2 + 2H2O
(c) BaCl2 + H2SO4 → BaSO4+ 2HCl
(d) none of the above
Answer:
(c) BaCl2 + H2SO4 → BaSO4+ 2HCl
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Question 11.
Choose the disproportional reaction among the following redox reactions.
(a) 3Mg (s) + N2(g) → Mg2N2 (s)
(b) P4 (s) + 3NaOH + 3H2O → PH3(g) + 3NaH2PO2 (aq)
(c) Cl2 (g) + 2Kl (aq) → 2KC1 (aq) + I2
(d) Cr2O3 (s) + 2Al (s) → A2O3 (s) + 2Cr (s)
Answer:
(b) P4 (s) + 3NaOH + 3H2O → PH3(g) + 3NaH2PO2 (aq)
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Question 12.
The equivalent mass of potassium permanganate in alkaline medium is
MnO4 + 2H2O + 3e → MnO2 + 4OH
(a) 31.6
(b) 52.7
(c) 79
(d) None of these
Answer:
(b) 52.7
The reduction reaction of the oxidizing agent(MnO4) involves gain of 3 electrons.
Hence the equivalent mass = (Molar mass of KMnO4) / 3 = 158.1 / 3 = 52.7

Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Question 13.
Which one of the following represents 180 g of water?
(a) 5 Moles of water
(b) 90 moles of water
(c) \(\frac{6.022 \times 10^{23}}{180}\) Molecules of water
(d) 6.022 × 1024 Molecules of water
Answer:
(d) 6.022 x 1024 Molecules of water
No. of moles of water present in 180 g
= Mass of water / Molar mass of water
= 180 g /18 g mol-1 = 10 moles
One mole of water contains
= 6.022 × 1023 water molecules
10 mole of water contains = 6.022 × 1023 × 10
= 6.022 × 1024 water molecules

Question 14.
7.5 g of a gas occupies a volume of 5.6 liters at 0°C and 1 atm pressure. The gas is …………
(a) NO
(b) N2O
(c) CO
(d) CO2
Answer:
(a) NO
7.5 g of gas occupies a volume of 5.6 liters at 273 K and 1 atm pressure Therefore, the mass of gas that occupies a volume of 22.4 liters –
\(\frac {7.5 g}{5.6 L}\) × 22. 4 L = 30g
Molar mass of NO (14 + 16) = 30g

Question 15.
The total number of electrons present in 1.7 g of ammonia is ………..
(a) 6.022 × 1023
(b) \(\frac{6.022 \times 10^{22}}{1.7}\)
(c) \(\frac{6.022 \times 10^{24}}{1.7}\)
(d) \(\frac{6.022 \times 10^{23}}{1.7}\)
Answer:
(a) 6.022 × 1023
No. of electrons present in one ammonia (NH3) molecule (7 + 3) = 10
No. of moles of ammonia = \(\frac {Mass}{Molar mass}\)
= \(\frac{1.7 \mathrm{g}}{17 \mathrm{g} \mathrm{mol}^{-1}}\) = 0.1 mol
No. of molecules present in 0ne ammonia
= 0.1 × 6.022 × 1023 = 6.O22 × 1022
No. of electrons present in 0.1 mol of ammonia
10× 6.022 × 1022 = 6.022 × 1023

Question 16.
The correct increasing order of the oxidation state of sulphur in the anions SO42-, SO32-, S2O42-,S2O62- is ………..
(a) SO32- < SO32- < S2O42- < S2O62-
(b) SO42- < S2O42- < S2O62-<SO32-
(c) S2O42- < SO32- < S2O62- < SO42-
(d) S2O62- < S2O42- < SO42- < SO32-
Answer:
(c) S2O42- < SO32- < S2O62- < SO42-
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Question 17.
The equivalent mass of ferrous oxalate is ……….
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
Answer:
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Question 18.
If Avogadro number were changed from 6.022 × 1023 to 6.022 × 1020, this would change ………..
(a) the ratio of chemical species to each other in a balanced equation
(b) the ratio of elements to each other in a compound
(c) the definition of mass in units of grams
(d) the mass of one mole of carbon
Answer:
(d) the mass of one mole of carbon

Question 19.
Two 22.4 liter containers A and B contains 8 g of O2 and 8 g of SO2 respectively, at 273 K and 1 atm pressure, then ……….
(a) number of molecules in A and B are the same
(b) number of molecules in B is more than that in A
(c) the ratio between the number of molecules in A to the number of molecules in B is 2 : 1
(d) number of molecules in B is three times greater than the number of molecules in A
Answer:
(c) The ratio between the number of molecules in A to number of molecules in B is 2 : 1

Question 20.
What is the mass of precipitate formed when 50 ml of 8.5% solution of Ag NO3 is mixed with 100 ml of 1.865% potassium chloride solution?
(a) 3.59 g
(b) 7 g
(c) 14 g
(d) 28 g
Answer:
(a) 3.59 g
AgNO3 + KCl → KNO3 + AgCl
Solution:
50 mL of 8.5% solution contains 4.25 g of AgNO3
No. of moles of AgNO3 present in 50 mL of 8.5% AgNO3 solution
= Mass / Molar mass = 4.25 / 170 = 0.025 moles
Similarly, No of moles of KCl present in loo mL of 1.865% KCl solution
= 1.865 / 74.5 = 0.025 moles
So total amount of AgCl formed is 0.025 moles (based on the stoichiometry calculator)
Amount of AgCl present in 0.025 moles of AgCl
= no. of moles × molar mass
= 0.025 × 143.5 = 3.59 g

Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Question 21.
The mass of a gas that occupies a volume of 612.5 ml at room temperature and pressure (25°C and 1 atm pressure) is 1.1g. The molar mass of the gas is ………..
(a) 66.25 g mol-1
(b) 44 g mol-1
(c) 24.5 g mol -1
(d) 662.5 g mol-1
Answer:
(b) 44 g mol-1
Solution:
No. of moles of a gas that occupies a volume of 6 12.5 ml at room temperature and pressure
(25° C and 1 atm pressure)
= 612.5 × 10-3 L/24.5 L mol-1
= 0.02 5 moles
We know that,
Molar mass = Mass / no. of moles
= 1.1 g/0.025 mol = 44 g mol-1

Question 22.
Which of the following contain same number of carbon atoms as in 6 g of carbon -12?
(a) 7.5 g ethane
(b) 8 g methane
(c) both (a) and (b)
(d) none of these
Answer:
(c) both (a) and (b)
Solution:
No. of moles of carbon present in 6 g of C – 12 = Mass / Molar mass
= 6/12 = 0.5 moles = 0.5 × 6.022 × 1023 carbon atoms.
No. of moles in 8 g of methane = 8 116 = 0.5 moles
= 0.5 × 6.022 × 1023 carbon atoms.
No. of moles in 7.5 g of ethane = 7.5 / 16 = 0.25 moles
= 2 × 0.25 × 6.022 × 1023 carbon atoms.

Question 23.
Which of the following compound( s) has/have a percentage of carbon same as that in ethylene (C2H4)?
(a) propene
(b) ethyne
(c) benzene
(d) ethane
Answer:
(a) propene
Solution:
Molar mass of carbon
Percentage of carbon in ethylene(C2H6) = Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
= \(\frac {24}{28}\) × 100 = 85.71%
Percentage of carbon in propene (C3H6) = \(\frac {24}{28}\) × 100 = 85.7 1%

Question 24.
Which of the following is/are true with respect to carbon – 12?
(a) relative atomic mass is 12 u
(b) oxidation number of carbon is +4 in all its compounds.
(c) I mole of carbon -12 contain 6.022 × 1022 carbon atoms.
(d) all of these
Answer:
(a) relative atomic mass is 12 u

Question 25.
Which one of the following is used as a standard for atomic mass?
(a) 6C12
(b) 7C12
(c) 6C13
(d) 6C14
Answer:
(a) 6C12

II. Write brief answer to the following questions

Question 26.
Define relative atomic mass.

On the basis of carbon, the relative atomic mass of an element is defined as the ratio of the mass of one atom of the element to the mass of l/12th mass of one atom of Carbon – 12.
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Question 27.
What do you understand by the term mole?
Answer:
The term ‘mole’ is used to represent 6.022 × 1023 entities (atoms or molecules or ions). One mole is the amount of substance of a system, which contains as many elementary particles as there are atoms in 12 g of carbon -12 isotope. The elementary particles can be molecules, atoms, ions, electrons, or any other specified particles.

Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Question 28.
Define equivalent mass.
Answer:
The equivalent mass of an element is the number of parts of the mass of an element which combines with or displaces 1.008 parts of hydrogen or 8 parts of oxygen or 35.5 parts of chlorine.

Question 29.
What do you understand by the term oxidation number?
Answer:
Oxidation number refers to the number of charges an atom would have in a molecule or an ionic compound, if electrons were transferred completely. The oxidation numbers reflect the number of electrons “transferred”.

Question 30.
Distinguish between oxidation and reduction.
Answer:
The oxidation number is defined as the imaginary charge left on the atom when all other atoms of the compound have been removed in their usual oxidation states that are assigned according to set of rules. A term that is often used interchangeably with oxidation number is oxidation state.

Grams to moles calculator is the best mole weight calculator.

Question 31.
Calculate the molar mass of the following compounds.

  1. urea [CO(NH2)2]
  2. acetone [CH3COCH3]
  3. boric acid [H3BO3]
  4. sulphuric acid [H2SO4]

Answer:
1. urea [CO(NH2)2]
Atomic mass of C =12
Atomic mass of O =16
Atomic mass of 2(N) = 28
Atomic mass of 4(H) = 4
∴ Molar mass of Urea = 60

2. Acetone [CH3COCH3]
Atomic mass of 3(C) = 36
Atomic mass of 1(0) = 16
Atomic mass of 6(H) = 6
∴ Molar mass of Acetone = 58

3. Boric acid [H3BO3]
Atomic mass of B = 10
Atomic mass of 3(H) = 3
Atomic mass of 3(O) = 48
∴ Molar mass of Boric acid = 61

4. Sulphuric acid 2[H2SO4]
Atomic mass of 2(H) = 2
Atomic mass of 1(S) = 32
Atomic mass of 4(O) = 64
∴ Molar mass of Sulphuric acid = 98

Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Question 32.
The density of carbon dioxide is equal to 1.977 kg m-3 at 273 K and 1 atm pressure. Calculate the molar mass of CO2
Answer:
Molecular mass = Density x Molar volume
Molar volume of CO2 = 2.24 x 10-2 m3
Density of CO2 = 1.977 kg m-3
Molecular mass of CO2 = 1.977 x 103 gm-3  x 2.24 x 10-2 m3
= 1.977 × 10-1 × 2.24 = 44 g

Question 33.
Which contains the greatest number of moles of oxygen atoms?

  1. 1 mol of ethanol
  2. 1 mol of formic acid
  3. 1 mol of H2O

Answer:
1. 1 mol of ethanol
C2H5OH (ethanol) – Molar mass = 24 + 6 + 16 = 46
46 g of ethanol contains 1 × 6.023 × 1023 number of oxygen atoms.

2. 1 mol of formic acid.
HCOOH (formic acid) – Molar mass = 2+12 + 32 = 46
46 g of HCOOH contains 2 × 6.023 × 1023 number of oxygen atoms.

3. 1 mol of H2O
H2O (water) – Molar mass = 2 + 16 = 18
18 g of water contains 1 × 6.023 × 1023 number of oxygen atoms.
∴ 1 mole of formic acid contains the greatest number of oxygen atoms.

Question 34.
Calculate the average atomic mass of naturally occurring magnesium using the following data

Isotope Isotopic atomic mass Abundance (%)
Mg24 23.99 78.99
Mg26 24.99 10
Mg25 25.98 11.01

Answer:
Isotopes of Mg.
Atomic mass = Mg24 = 23.99 x \(\frac {783. 99}{100}\) = 18.95
Atomic mass = Mg26 = 24.99 x \(\frac {10}{100}\) = 2.499
Atomic mass = Mg25 = 25.98 x \(\frac {11.01}{100}\) = 2.860
Average Atomic mass = 24.309
Average atomic mass of Mg = 24.309

Question 35.
In a reaction x + y + z2 → xyz2, identify the limiting reagent if any, in the following reaction mixtures.
(a) 200 atoms of x + 200 atoms of y + 50 molecules of z2
(b) 1 mol of x + 1 mol of y + 3 mol of z2
(c) 50 atoms of x + 25 atoms of y + 50 molecules of z2
(d) 2.5 mol of x + 5 mol of y + 5 mol of z2
Answer:
x + y + z2
(a) 200 atoms of x + 200 atoms of y + 50 molecules of z2 According to the reaction, 1 atom of x reacts with one atom of y and one molecule of z to give product. In the case (a) 200 atoms of x, 200 atoms of y react with 50 molecules of z2 (4 part) i.e. 50 molecules of z2 react with 50 atoms of x and 50 atoms of y. Hence z is the limiting reagent.

(b) 1 mol of x + 1 mol of y + 3 mol of z2
According to the equation 1 mole of z2 only react with one mole of x and one mole of y. If 3 moles of z2 are there, z is limiting reagent.

(c) 50 atoms of x + 25 atoms of y + 50 molecules of z2
25 atoms of y react with 25 atoms of x and 25 molecules of z2. So y is the limiting reagent.

(d) 2.5 mol of x + 5 mol of y + 5 mol of z2
2.5 mol of x react with 2.5 mole of y and 2.5 mole of z2. So x is the limiting reagent.

Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Question 36.
Mass of one atom of an element is 6.645 × 10-23 g. How many moles of element are there in 0.320 kg?
Answer:
Mass of one atom of an element = 6.645 × 10-23 g = Atomic mass.
Mass of given element = 0.320 kg
Number of moles = Atomic mass
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
= 48.156 x 10-23
= 4.8156 x 10-24 moles.

Question 37.
What is the difference between molecular mass and molar mass? Calculate the molecular mass and molar mass for carbon monoxide.
Answer:
Molecular mass is defined as the ratio of the mass of a molecule to the unified atomic mass unit.
The relative molecular mass of any compound can be calculated by adding the relative atomic masses of its constituent atoms.
Molar mass is defined as the mass of one mole of a substance.
The molar mass of a compound is equal to the sum of the relative atomic masses of its constituents expressed in g mol-1.
Molecular mass of Carbon monoxide
= (1 × Atomic mass of carbon) + ( 1 × Atomic mass of oxygen)
= (1 × 12) +(1 × 16) = 28 u.
Molar mass of Carbon monoxide
= (1 × Atomic mass of carbon) + ( 1 × Atomic mass of oxygen)
= (1 × 12) + (1 × 16) = 28 g mol-1.

Question 38.
What is the empirical formula of the following?

  1. Fructose (C6H12O6) found in honey
  2. Caffeine (C8H10N4O2) a substance found in tea and coffee.

Answer:
1. Fructose (C6H12O6)
Empirical formula is the simplest formula. So it is divided by 6 and so empirical formula is CH2O.

2. Caffeine (C8H10N4O2)
Simplified formula = \(\frac {molecular formula}{2}\)
Empirical formula = C4H5N2O.

Question 39.
The reaction between aluminium and ferric oxide can generate temperatures up to 3273 K and is used in welding metals. (Atomic mass of AC = 21 u Atomic mass of 0 = 16 u) 2Al + Fe2O2 → Al2O3 + 2Fe; If, in this process, 324 g of aluminium is allowed to react with 1.12 kg of ferric oxide.

  1. Calculate the mass of Al2O3 formed.
  2. How much of the excess reagent is left at the end of the reaction?

Answer:
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
1. As per the balanced equation 54 g A1 is required for 112 g of iron and 102 g of Al2O3.
54 g of Al gives 102 g of Al2O3.
∴ 324 g of Al will give \(\frac{102}{54}\) x 324 = 612 g of Al2O3.

2. 54 g of Al requires 160 g of Fe2O3 for welding reaction.
∴ 324 g of Al will require \(\frac {160}{54}\) x 324 = 960 g of Fe2O3.
∴ Excess Fe2O3 – Unreacted Fe2O3 = 1120 – 960 = 160 g
160 g of excess reagent is left at the end of the reaction.

Question 40.
How many moles of ethane is required to produce 44 g of CO2 (g) after combustion.
Answer:
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
∴ 44g of CO2 = I mole of CO2
2 moles of CO2 is produced by 1 mole of ethane.
∴ 1 mole of CO2 will be produced by = ?
∴ To produce 1 mole of CO2, the required mole of ethane is = \(\frac {1}{2}\) x 1 = 0.5 mole of ethane.

Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Question 41.
Hydrogen peroxide is an oxidizing agent. It dioxides ferrous ion to ferric ion and reduced itself to water. Write a balanced equation.
Answer:
H2O2 – Oxidizing agent
Fe2+ + H2O2 → Fe3+ + H2O (Acetic medium)
Ferrous ion is oxidized by H2O2 to Ferric ion.
The balanced equation is Fe2+ → Fe3+ + e x 2
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Question 42.
Calculate the empirical and molecular formula of a compound containing 76.6% carbon, 6.38 % hydrogen and rest oxygen its vapour density is 47.
Answer:
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
Empirical formula = C6H6O
Va-pour density 47
∴ Molecular mass = 2 x vapor density = 2 x 47 = 94
Molecular formula Empirical formula x n
Molecular mass x n
n = \(\frac { Molecular mass }{ Empirical formula mass }\) = \(\frac {94}{94}\) = 1
∴ Molecular formula = C6H6O

Question 43.
A Compound on analysis gave Na = 14.31% S = 9.97% H = 6.22% and O = 69.5% calculate the molecular formula of the compound if all the hydrogen in the compound is present in combination with oxygen as water of crystallization, (molecular mass of the compound is 322).
Answer:
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
All H combines with 10 oxygen atoms to form as 10H2O.
So the empirical formula is Na2SO4 .10H2 O
Empirical formula mass = (23 x 2) + (32 x 1) + (16 x 4) + (10 x 18)
= 46 + 32 + 64 + 180 = 322
n = \(\frac { Molecular mass }{ Empirical formula mass }\) = \(\frac {322}{322}\) = 1
Molecular formula = Na2SO4. 10H2O

Question 44.
Balance the following equations by oxidation number method

  1. K2Cr2 O7 + KI + H2SO2 → K2SO4 + Cr2(SO4)3 + I2 + H2O
  2. KMnO4 + Na2SO3 → Mn02 + Na2SO4 + KOH
  3. Cu+ HNO3 → Cu(N03)2 + NO2 + H2O
  4. H2C2O4 + KMnO4 + H2SO4 → K2SO4 + MnSO4 + CO2 + H2O

Answer:
1. K2Cr2 O7 + KI + H2SO2 → K2SO2 + Cr2(SO4)3 + I2 + H2O
Step – 1.
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
Step – 2
K2Cr2 O7 + 6KI + H2SO4 → K2SO4 + Cr2(SO4)3 + 3I2 + H2O
Step – 3
To balance other atoms
K2Cr2 O7 + 6KI + H2SO4 → 4K2SO4 + Cr2(SO4)3 + 3I2 + H2O
Step – 4
K2Cr2 O7 + 6KI + 7H2SO4 → 4K2SO4 + Cr2(SO4)3 + 3I2 + 7H2O

2. KMnO4 + Na2SO3 → MnO2 + Na2SO4 + KOH (Alkaline medium)
Step – 1
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
Step – 2
2KMnO4 + 3Na2SO3 → 2MnO2 + 3Na2SO4 + KOH
Step – 3
balancing potassium, KOH is multiplied by 2
2KMnO4 + 3Na2SO3 → 2MnO2 + 3Na2SO4 + KOH
Step – 4
To balance H atom, H20 is added on reactant side.
2KMnO4 + 3Na2SO3 + H2O → 2MnO2 + 3Na2SO4 + KOH

3. Cu + HNO3 → Cu(NO3)2 + NO2 + H2O
Step – 1
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
Step – 2
Cu + HNO3 → Cu(NO3)2 + NO2 + H2O
Step – 3
To balance Nitrogen, 2HNO3 is multiplied by 2 and NO2 is multiplied by 2
Cu + 4HNO3 → Cu(NO3)2 + 2NO2 + H2O
Step 4.
To balance oxygen, H2O is multiplied by 2
Cu + 4HNO3 → Cu(NO3)2 + 2NO2 + 2H2O

4. H2C2O4 + KMnO4 + H2SO4 → K2SO4 + MnSO4 + CO2 + H2O
Step – 1
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
Step – 2
5 H2C2O4 + KMnO4 + H2SO4 → K2SO4 + MnSO4 + 10 CO2 + H2O
Step – 3
To balance K, KMnO4 and MnSO4 are multiplied by 2
5 H2C2O4 + 2KMnO4 + H2SO4 → K2SO4 + 2MnSO4 + 10 CO2 + H2O
Step – 4
To balance O and H, H2O and H2SO4 are multiplied by 3 and 6.
5 H2C2O4 + 2KMnO4 + 3H2SO4 → K2SO4 + 2MnSO4 + 10 CO2 + 8H2O

Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Question 45.
Balance the following equations by ion-electron method.

  1. KMnO4 + SnCl2  + HCl → MnCl2  + SnCl4  + H2O + KCl
  2. C2O42- + Cr2 O7 2- → Cr 3+ + CO2  (in acid medium)
  3. Na2S2O3 + I2 → Na2S4O6 + NaI (in acid medium)
  4. Zn + NO3 → Zn2+ + NO

Answer:
1. KMnO4 + SnCl2 + HCl → MnCl3 + SnCl3 +H2O + KCl
Oxidation half reaction: (loss of electrons)
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Reduction half reaction: (gain of electrons)
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
Add H2O to balance oxygen atoms.
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
Add HCl to balance hydrogen atoms
KMnO4 + 5e + 8HCl → MnCl2 + 4H2O ………(4)
To equalize the number of electrons equation (1) x 5 and equation (2) x 2
5SnCl2 → 5SnCl4 + 10e
2KMnO4 + 16HCl + 10e → 2MnCl2 + 4H2O + 2KCl
2KMnO4 + 5SnCl2 + 16HCl → 5SnCl4 + 2MnCl2 + 4H2O + 2KCl

2. C2O42- + Cr2 O72- → Cr 3+ + CO2  (in acid medium)
Oxidation half reaction:
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
Reduction half reaction:
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
To balance oxygen atoms, H2O is added on RHS of equation (2)
Cr2O72- + 6e → 2Cr3+ + 7 H2O ……….(3)
To balance Hydrogen atoms, H+ is added on LHS of equation (1)
C2O42- + 14H+ → 2CO2 + 2e ……..(4)
To equalize the number of electrons gained and lost, multiply the equation (4) x 3.
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

3. Na2S2O3 + I2 → Na2S4O6 + NaI (in acid medium)
Oxidation half reaction: (Loss of electron)
Na2S2O3 → Na2S4O6 + 2e2- ……..(1)
Reduction half reaction: (Gain of electron)
I2 + 2e2-→ 2NaI …………(2)
Adding (1) and (2)
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
To balance oxygen,
2Na2S2O3 + I2 → Na2S2O2 + 2NaI

In acidic medium
4. Zn + NO3 → Zn2+ + NO
Half reactions are –
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Samacheer Kalvi 11th Chemistry Basic Concepts of Chemistry and Chemical Calculations In Text Questions – Evaluate Yourself

Question 1.
By applying the knowledge of chemical classification, classify each of the following Into elements, compounds or mixtures.

  1. Sugar
  2. Sea water
  3. Distilled water
  4. Carbon dioxide
  5. Copper wire
  6. Table salt
  7. Silver plate
  8. Naphthalene balls

Answer:

Elements Compounds Mixtures
Copper wire (Cu)
Silverplate (Ag)
Sugar
Distilled water Carbon dioxide Naphthalene balls
Seawater
Table salt

Question 2.
Calculate the molar mass of the following.

  1. Ethanol (C2H5OH)
  2. Potassium permanganate (KMnO4)
  3. Potassium dichromate (K2Cr2O7)
  4. Sucrose (C12H22O11)

Answer:
(1) Ethanol (C2H5OH)
Molar mass = (2 × 12) + (6 × 1) + (1 × 16)
= 24 + 6+16
= 46 g mol-1

(2) Potassium permanganate (KMnO4)
Molar mass = 39 + 55 + (4 × 16)
= 39 + 55 + 64
= 158 g mol-1

(3) Potassium dichromate (K2Cr2O7)
Molar mass = (39 × 2) + (2 × 52) + (7 × 16)
= 78 + 104 + 112
= 294 g mol-1

(4) Sucrose (C12H22O11)
Molar mass = (12 × 12) + (22 × 1) + (11 × 16)
= 144 + 22 + 176
= 342 g mol-1

Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Question 3.
(a) Calculate the number of moles present in 9 g of ethane.
Answer:
Mass of ethane = 9 g
The molar mass of ethane C2H6 = 30 g mol-1
No. of moles = \(\frac {Mass}{Molar mass}\) = \(\frac {9}{30}\) = 0.3 mol.

(b) Calculate the number of molecules of oxygen gas that occupies a volume of 224 ml at 273 K and 3 atm pressure.
Answer:
Molar volume of oxygen = 22400 ml.
22400 ml of oxygen contains 6.023 x 1023 molecules.
224 ml of oxygen contain \(\frac{6.023 \times 10^{23}}{22400}\) x 224
\(\frac{6.023 \times 10^{23}}{100}\) = 6.023 × 1021

Question 4.
(a) 0.456 g of metal gives 0.606 g of its chloride. Calculate the equivalent mass of the metal.
Answer:
Mass of the metal = W1 = 0.456 g.
Mass of the metal chloride = W2 = 0.606 g.
∴Mass of chlorine = W2 – W1 = 0.606 – 0.456 = 0.15 g
0.15 g of chlorine combine with 0.456 g of metal.
∴ 35.46 g of chlorine will combine with \(\frac {0.456}{0.15}\) x 35.46 = 107.79 g eq-1

(b) Calculate the equivalent mass of potassium dichromate. The reduction half – reaction in acid medium is –
Cr2O72- + 14H+ +6e → 2 Cr3+ + 7H2O
Answer:
Cr2O72- + 14H+ +6e → 2 Cr3+ + 7H2O
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
Molar mass of K2Cr2O7 = 294.18
∴ Equivalent mass of K2Cr2O7 = \(\frac { 294.18}{6}\) = 49.03

Question 5.
A Compound on analysis gave the following percentage composition C = 54.55%, H = 9.09%, O = 36.36%. Determine the empirical formula of the compound.
Answer:
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
Empirical formula = C2H4O

Question 6.
Experimental analysis of a compound containing the elements x,y,z on analysis gave the following data, x = 32 %, y = 24 %, z = 44 %. The relative number of atoms of x, y and z are 2,1 and 0.5, respectively. (Molecular mass of the compound is 400 g) Find out.

  1. The atomic masses of the element x,y,z.
  2. Empirical formula of the compound and
  3. Molecular formula of the compound.

Answer:
Element x = 32% ; y = 24% ; z = 44%
Relative number of atoms x = 2 ; y = 1 ; z = 0.5
Molar mass of the compound = 400 g.

1. Atomic mass of the element.
Relative number of atoms Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
∴  Atomic mass Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
Atomic mass x = \(\frac {32}{2}\) = 16
Atomic mass y = \(\frac {24}{1}\) = 24
Atomic mass z = \(\frac {44}{0.5}\) = 88
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

2. Empirical formula of the compound x4 y2 Z1
Molecular mass of the compound = 400
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations = \(\frac {400}{200}\) = 2

3. Molecular formula of the compound = x8 y4 z2

Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Question 7.
The balanced equation for a reaction is given below 2x + 3y → 41 + m When 8 moles of x react with 15 moles of y, then –

  1. Which is the limiting reagent?
  2. Calculate the number of products formed.
  3. Calculate the amount of excess reactant left at the end of the reaction.

Answer:
2 x + 3 y → 41 + m

1. 2x reacts with 3y to give products.
5x reacts with 15y means, y is the excess because 8 moles of x should react within 4 x 3y = 12y moles of y to give products. In this reaction 15y moles are used. Therefore, 3 moles of y is excess and it is the limiting agent.

2. When 8 moles of x react with 12 moles of y, the product formed will be 4 x 41 i.e. 161 and 4m as product.
8x + 12y → 161 + 4m

3.  At the end of the reaction, the excess reactant left in 3 moles of y.

Question 8.
Balance the following equation using the oxidation number method
AS2 S3  + HNO3 + H2O → H3ASO4 + H2SO4 + NO
Answer:
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
To balance oxygen and sulphur, H2O and H2SO4 are added.
3AS2S3 + 2HNO3 + H2O → 6H3ASO4 + 2NO + H2SO2
3AS2S3 + 28HNO3 + 4H2O → 6H3ASO4 + 28NO + 9H2SO4

Samacheer Kalvi 11th Chemistry Solutions Basic Concepts of Chemistry and Chemical Calculations Textual Calculations based on Stolchlometry Solved

Question 1.
How many moles of hydrogen are required to produce 10 moles of ammonia?
Answer:
The balanced stoichiometric equation fòr the formation of ammonia is
N2(g) + 3H2(g) → 2NH2(g)
4s per the stoichiometric equation, to produce 2 moles of ammonia, 3 moles of hydrogen are required.
∴ to produce 10 moles of ammonia,
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
= 15 moles of hydrogen are required.

Question 2.
Calculate the amount of water produced by the combustion of 32 g of methane.
Answer:
CH4(g) + 2O2(g) → CO2(g) + 2H2O(g)
As per the stoichiometric equation,
Combustion of 1 mole (16 g) CH4 produces 2 moles (2 x 18 = 36 g) of water.
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
Combustion of 32 g CH4 produces
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Question 3.
How much volume of carbon dioxide is produced when 50 g of calcium carbonate is heated completely under standard conditions?
Answer:
The balanced chemical equation is,
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
As per the stoichiometric equation,
1 mole (100g) CaCO3 on heating produces 1 mole CO2
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
At STP, 1 mole of CO2 occupies a volume of 22.7 litres
At STP, 50 g of CaCO3 on heating produces,
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
= 11.35 litres of CO2

Question 4.
How much volume of chlorine is required to form 11.2 L of HCl at 273 K and 1 atm pressure ?
Answer:
The balanced equation for the formation of HCl is,
H2 (g) + Cl2 (g) → 2 HCl (g)
As per the stoichiometric equation, under given conditions,
To produce 2 moles of HCl, 1 mole of chlorine gas is required.
To produce 44.8 liters of HCl, 22.4 liters of chlorine gas are required
∴ To produce 11.2 liters of HCl,
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
= 5.6 litres of chlorine are required.

Question 5.
Calculate the percentage composition of the elements present in magnesium carbonate. How many kilograms of CO2 can be obtained by heating 1 kg of 90 % pure magnesium carbonate.
Answer:
The balanced chemical equation is
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
Molar mass of MgCO3 is 84 g mol-1.
84 g MgCO3 contain 24 g of Magnesium.
∴ 100 MgCO3 contain
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
= 28.57 g Mg i.e. percentage of magnesium = 28.57 %.
84 g MgCO3 contain 12 g of carbon
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
= 14.29 g of carbon
Percentage of carbon = 14.29 %.
84 g MgCO3 contain 48 g of oxygen
∴ 100 g MgCO3 contains
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
= 57.14 g of oxygen.
∴ Percentage of oxygen = 57.14 %.
As per the stoichiometric equation,
84 g of 100 % pure Mg CO3 on heating gives 44 g of CO2.
∴1000 g of 90 % pure Mg CO3 gives
\(\frac {44 g}{84 g x 100 %}\) x 90 % x 1000 g
= 471.43 g of CO2
= 0. 471 kg of CO2

Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Question 6.
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
(1) If the entire quantity of all the reactants is not consumed in the reaction which is the limiting reagent ?
(2) Calculate the quantity of urea formed and un reacted quantity of the excess reagent. The balanced equation is
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
Answer:
(1) The entire quantity of ammonia is consumed in the reaction. So ammonia is the limiting reagent. Some quantity of CO2 remains unreacted, so CO2 is the excess reagent.

(2) Quantity of urea formed = number of moles of urea formed x molar mass of urea
= 19 moles x 60 g mol-1
= 1140 g = 1.14 kg
Excess reagent leftover at the end of the reaction is carbon dioxide. Amount of carbon dioxide leftover = number of moles of CO2 left over x molar mass of CO2
= 7 moles x 44 g mol-1 = 308 g.
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Samacheer Kalvi 11th Chemistry Solutions Basic Concepts of Chemistry and Chemical Calculations Additional Questions Solved

I. Choose the correct answer from the following

Question 1.
Which one of the following is the standard for atomic mass?
(a) 1H1
(b) 66C12
(c) 6C14
(d) 8O16
Answer:
(b) 66C12
Hint:
Standard element used to determine atomic mass is 6 Cl2

Question 2.
One mole of CO2 contains ………….
(a) 6.023 x 1023 atoms of C
(b) 6.023 x 1023 atoms of O
(c) 18.1 x 1023 molecules of CO2
(d) 3g atoms of CO2
Answer:
(a) 6.023 x 1023 atoms of C
Hint:
One mole of any substance contains an Avogadro number of atoms. In this carbon one mole is present and oxygen two atoms are present. So, 6.023 x 1023 atoms of C is correct.

Question 3.
The largest number of molecules is in
(a) 54 g of nitrogen pentoxide
(b) 28 g of carbon dioxide
(c) 36 g of water
(d) 46 g of ethyl alcohol
Answer:
(c) 36 g of water
Hint:(a) 54 g of N2O5
N2O5 = Molecular mass = 28 + 80 = 108
108 g of N2O5 contains 6.023 x 1023 molecules.
∴ 54 g of N2O5 will contain \(\frac{6.023 \times 10^{23}}{108}\) x 54 = 3.0115 x 1023 molecules.

(b) 28 g of CO2
CO2 = Molecular mass = 12 + 32 = 44
44 g of CO2 contains 6.023 x 1023 molecules.
∴ 28 g of CO2 will contain \(\frac{6.023 \times 10^{23}}{44}\) x 28 = 3.832 x 1023 molecules.

(c) 36 g of H2O
H2O = Molecular mass = 2 + 16 = 18
18 g of H2O contains 6.023 x 1023 molecules.
∴ 36 g of H2O will contain \(\frac{6.023 \times 10^{23}}{18}\) x 36 = 12.046 X 1023molecules.

(d) 46 g of C2H5OH
C2H5OH = Molecular mass = 24 + 6 + 16 = 46
46 g of C2H5OH contains 6.023 x 1023 molecules.
So, among the 4, 36 g of water contain the largest number of molecules as 12.046 x 1023.

Question 4.
The number of moles of H2 in 0.224 liter of hydrogen gas at STP is …………..
(a) 1
(b) 0.1
(c) 0.01
(d) 0.001
Answer:
(c) 0.01
22.4 liter of hydrogen gas at STP contains 1 mole.
∴ 0.224 liter of hydrogen gas at STP will contain \(\frac{1}{22.4}\) x 0.224 = 0.01

Question 5.
10 g of hydrogen and 64 g of oxygen were filled in a steel vessel and exploded. The amount of water produced in this reaction will be ………..
(a) 3 mol
(b) 4 mol
(c) 1 mol
(d) 2 mol
Answer:
(b) 4 mol
10 g of H2 + 64 g of O2 → water
2H2 + O2 → 2H2O
4 g of hydrogen reacts with 32 g of oxygen. So 10 g of hydrogen will react with 80 g of oxygen. But we have given the amount of oxygen only 64 g. It means, here oxygen is the limiting agent. Now all the oxygen react with 8 g of hydrogen and form 4 moles of water.

Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Question 6.
6.023 x 1020 molecules of urea are present in 100 ml of its solution. The concentration of the solution is –
(a) 0.02 M
(b) 0.1 M
(c) 0.01 M
(d) 0.001 M
Answer:
(c) 0.01 M
100 ml of solution contain 6.023 x 1020 molecules.
6.023 x 1023 molecules in 1000 ml = 1 M.
∴ 6.023 x 1020 molecules in 1000 ml =  Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
= 1020 x 10-23 = 10-3
10-3 moles present in 100 ml.
∴ In 1000 ml the moles present is = \(\frac{10^{-3}}{100}\) x 1000 = 10-2 moles
Concentration = 0.01 M

Question 7.
Two containers A and 13 of the equal volume contain 6 g of O2 and SO2 at 300 K and 1 atm. Then
(a) No. of molecules in A is less than that in B
(b) No. of molecules in A is more than that in B
(c) No. of molecules in A and B are the same
(d) none of these
Answer:
(b) No, of molecules in A is more than that in B
O2 = Mass = 6 g
Molar mass = 32 g
32 g of O2 contains 6.023 x 1023 molecules.
∴ 6 g of O2 will contain = 6.023 X 1023 x 6 = 1.129 x 1023 molecules.
SO2 = Mass = 6 g
Molar mass = 64 g
64 g of SO2 contains 6.023 x 1023 molecules.
∴ 6 g of SO2 will contain 6.023 x 1023 x 6 = 0.5646 x 1023 molecules.
∴ The number of molecules in A is more than that in B.

Question 8.
The number of molecules in 16 g of methane is ……….
(a) 3.023 x 1023
(b) 6.023 x 1023
(c) 16 / 6.023 x 1023
(d) 6.023 / 3 x 1023
Answer:
(b) 6.023 x 1023
Hint:
Methane: CH4
Molecular mass 12 + 4 = 16
16 g of methane contains Avogadro’s number of molecules 6.023 x 1023 molecules.

Question 9.
The number of atoms in 4.25 g of ammonia is …………..
(a) 1 x 1023
(b) 2 x 1023
(e) 4 x 1023
(d) 6 x 1023
Answer:
(d) 6 x 1023
Hint:
Ammonia = NH3 (4 atoms)
Molecular mass = 14 + 3 = 17
17 g of Ammonia contains 6.023 x 1023 atoms.
∴ 4.25 g of Ammonia will contain 6.0231; 1023 x 4.25 = 1.5055 x 1023 molecules.
∴ 1.5055 x 1023 molecules will contain 4 x 1.5 x 1023 = 6 x 1023 molecules.

Question 10.
The number of molecules in a drop of water (0.0018 ml) at room temperature is ……….
(a) 6.02 x 1023
(b) 1.084 x 1023
(c) 4.84 x 1023
(d) 6.02 x 1023
Answer:
(a) 6.02 x 1023
Hint:
0.0018 ml – drop of water = 0.0018 g
H2O = molecular mass = 18 g.
Number of molecules in 18 g = 6.023 x 1023
∴ Number of molecules in 0.0018 g 6.023 x 1023 x 0.0018 = 6.023 x 1023 x 105
= 6.023 x 1019 molecules.
or
Density of water at 25°C = 997.0479 g / L
Mass of 0.0018 ml (or) 0.00 18 x 10-3 L
= D x V
= 997.05 x 0.0018 x 10-3
= 1.795 x 10-3 g
Molar mass of water = 18 g
Mole = \(\frac{Mass}{Molecular mass}\) = \(\frac{1.795 \times 10^{-3}}{18}\)
= 9.971 x 10-5
∴ Number of molecules in 0.0018 ml = moles x Avogadro number
= 9.971 x 10-5 x 6.023 x 1023
= 6 x 1019 molecules.

Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Question 11.
7.5 g of gas occupies 5.6 liters of volume at STP. The gas ……….
(a) NO
(b) N2O
(c) CO
(d) CO2
Answer:
(a) NO
Hint:
22.4 liters = 1 mole
5.6 liters = \(\frac {1}{22.4}\) x 5.6 = 0.25 mole.
NO = molar mass = 14 + 16 = 30 g = 1 mole
N2O = molar mass = 28 + 16 = 44g = 1 mole
CO = molar mass = 12 + 16 = 28 g = 1 mole
CO2=molar mass = 12 + 32 = 44g = 1 mole
Among the four gases, 0.25 mole = 7.5 g is equal to NO gas.

Question 12.
The mass in grams of 0.45 mole of CO2 ions ……….
(a) 1.8
(b) 40
(c) 36
(d) 18
Answer:
(d) 18
Hint:
Ca = Atomic mass = 40
Ca → Ca2+ + 2e
41 g of Ca = 1 mole (for Ca2+ Atomic mass remains same)
1 mole of Ca2+ = 40 g
∴ 0.45 mole of Ca2+ = \(\frac {40}{1}\) x 0.45 = 18g

Question 13.
The mass of one molecule of HI in grams is ……….
(a) 2.125 x 10-22
(b) 128
(c) 127
(d) 6.02 x 10-23
Answer:
(b) 128
Hint:
HI = 1 mole = 1 + 127 = 128 g

Question 14.
Avogadro’s number is the number of molecules present in ……….
(a) 1 g of molecule
(b) 1 g atom of molecule
(c) gram molecular mass
(d) I lit of molecule
Answer:
(c) gram molecular mass
by definition (c) is correct

Question 15.
Which of the following contains same number of carbon atoms as are in 6.0 g of carbon (C-12)?
(a) 6.0 g ethane
(b) 8.0 g methane
(c) 21.0 g Propane
(d) 28.0 g CO
Answer:
(b) 8.0 g methane

Hint:
(a) 6.0 g of ethane (C2H6)
C2H6 = molar mass = 24 + 6 = 30 g
30 g of ethane contains 2 x 6.023 x 1023 Carbon atoms.

(b) 8.0 g of methane (CH4)
CH4 molar mass = 12 + 4 = 16g
16 g of methane contains 6.023 x 1023 Carbon atoms.

(c) 21.0 g of propane (C3H8)
C3H8 = molar mass = 36 + 8 = 44 g
44 g of propane contains 3 x 6.023 x 1023 Carbon atoms.

(d) 28.0 g of Carbon monoxide (CO)
CO = molar mass = 12+ 16 = 28 g
28 g of Carbon monoxide contains 6.023 x 1023 Carbon atoms.
6.0 g of Carbon contains = 6.023 x 10 x 6 = 3.0115 x 1023 Carbon atoms.
Among the (a), (b), (c), (d) – 8 g of CH4 contains x 8 = 3.0115 x 1023 Carbon atoms.

Question 16.
The equivalent mass of KMnO4 when it is converted to MnSO4 is equal to molar mass divided by ………..
(a) 6
(b) 4
(c) 5
(d) 2
Answer:
(c) 5
Hint:
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Question 17.
How many equivalents of Sodium sulphate are formed when Sulphuric acid is completely neutralized with a base NaOH?
(a) 0.2
(b) 2
(e) 0.1
(d) 1
Answer:
(d) 1
Hint:
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Question 18.
Cl2 changes to Cl and ClO in cold NaOH. Equivalent mass of Cl2 will be ………..
(a) Molar mass / 2
(b) Molar mass / 1
(c) Molar mass / 3
(d) 2 x Molar mass / 2
Answer:
(a) Molar mass / 2
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Question 19.
Equivalent mass of KMnO4 in acidic medium, concentrated alkaline medium and dilute basic medium respectively are M, M, M. Reduced products can be ……………
(a) MnO2, MnO22-, Mn2+
(b) MnO2, Mn2+, MnO42-
(c) Mn2+, MnO2, MnO42-
(d) Mn2+, MnO42-, MnO2
Answer:
(c) Mn2+, MnO2, MnO42-
Hint:
MnO4 + 8H+ + 5e → Mn2+ + 4H2O (acidic medium)
MnO4 + 4H+ + 3e → MnO2 + 2H2O (concentrated basic medium)
MnO4 + e → MnO42- (dilute basic medium)

Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Question 20.
The empirical formula of hydrogen peroxide is
(a) HO
(b) H2O
(e) H3O
(d) H2O2
Answer:
(a) HO
Hint:
Molecular formula of hydrogen peroxide = H2O2
H2O2 ÷ 2 = HO = Empirical formula.

Question 21.
Molecular mass =
(a) Vapour Density × 2
(b) Vapour Density ÷ 2
(c) Vapour Density × 3
(d) Vapour Density
Answer:
(a) Vapour Density × 2

Question 22.
20.0 g of a magnesium carbonate sample decomposes on heating to give carbon dioxide and 8.0 g magnesium oxide. What will be the percentage of purity of magnesium carbonate in the sample?
(a) 60
(b) 84
(e) 75
(d) 96
Answer:
(b) 84
Hint:
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
84 g of MgCO3 gives 40 g of MgO. (100% purity)
20 g of MgCO3 will give = \(\frac{40 \times 20}{84}\) = 9.52 g
9.52 g of MgO is given by 100% pure MgCO3.
8.0 g of MgO will be given by = \(\frac{100 \times 8}{9.52}\) = 84.03%

Question 23.
What is the mass of the precipitate formed when the preparation of alkyl halides 50 ml of 16.9 % solution of AgNO3 is mixed with 50 ml of 5.8 % NaCl solution?
(a) 7 g
(b) 14 g
(c) 28 g
(d) 35 g
Answer:
(a) 7 g
Hint:
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Question 24.
When 22 L of hydrogen gas is mixed with 11.2 L of chlorine gas, each at STP, the moles of HCl gas formed is equal to ……….
(a) 2
(b) 0.5
(c) 1.5
(d) 1
Answer:
(d) 1
Hint:
H2 + Cl2 → 2HCl
22 liters + 11.2 litres
1 mole + \(\frac {1}{2}\) mole = 1 mole of HCl and \(\frac {1}{2}\) mole of H2 is remained.

Question 25.
5.6 L of a gas at STP are found to have mass of 11 g. The molecular mass of the gas is
(a) 36
(b) 48
(c) 40
(d) 44
Answer:
(d)44
Hint:
5.6 L of gas has the mass of 11 g.
∴ 22.4 L of gas will have the mass \(\frac {11}{5.6}\) x 22.4 = 44

Question 26.
Oxidation number f Fluorine in all compounds is ……….
(a) +1
(b) -1
(c) 0
(d) -2
Answer:
(b) -1

Question 27.
In redox reaction which of the following is true?
(a) Number of electrons lost is more than number of electrons gained
(b) Number of electrons lost is less than number of electrons gained
(c) Number of electrons lost s equal number of electrons gained
(d) No transfer and gain of electrons during the reaction.
Answer:
(c) Number of electrons lost is equal number of electrons gained

Question 28.
Which of the following is a mono-atomic molecule?
(a) Hydrogen
(b) Oxygen
(c) Sodium
(d) Ozone
Answer:
(c) Sodium

Question 29.
Which one of the following is a diatomic molecule?
(a) Ozone
(b) Copper
(c) Hydrogen
(d) Gold
Answer:
(c) Hydrogen

Question 30.
The value of Avogadro Number N is equal to ……….
(a) 2.24 x 10-2L
(b) 22400 cm3
(c) 6.023 x 10-23
(d) 6.023 x 1023
Answer:
(d) 6.023 x 1023

Question 31.
46 g of ethanol contains ……….
(a) 2 x 6.023 x 1023 C atoms
(b) 3 x 6.023 x 1023 atoms
(c) 9 x 6.023 x 1023 H atoms
(d) 6.023 x 1023 Carbon atoms
Answer:
(a) 2 x 6.023 x 1023 C atoms
Hint:
C2H5OH = Molecular mass = (12 x 2) + (1 x 6) + (1 x 16)
= 24 + 6 + 16
= 46
2 Carbon atoms are present.
∴ 2 x 6.023 x 1023 C atoms is correct.

Question 32.
The mass of one mole of CaCl2 is ……….
(a) 55.5 g mol-1
(b) 111 g mol-1
(c) 222 g mol -1
(d) 77.5 g mol-1
Answer:
(b) 111 g mol-1
Hint:
CaCl2 = Mass = 40 + 71 = 111 g mol-1

Question 33.
22 g of CO2 contains molecules of CO2
(a) 6.023 x 1023
(b) 6.023 x 1023
(c) 3.0115 x 1023
(d) 3.0115 x 1023
Answer:
(c) 3.0115 x 1023
Hint:
44 g of CO2 contains 6.023 x 1023 molecules.
∴ 22 g of CO2 will contain = \(\frac{6.023 \times 10^{23}}{44}\) x 22 = 3.0115 x 1023

Question 34.
The formula weight of ethanol (C2H5OH) is ……….
(a) 56.5 amu
(b) 16 amu
(c) 60 amu
(d) 46 amu
Answer:
(d) 46 amu
Hint:
Formula weight of C2H5OH = (12 x 2) + (6 x 1) + (1 x 16)
= 24 + 6 + 16 = 46 amu

Question 35.
The number of moles of ethane in 60 g is ……….
(a) 2
(b) 4
(c) 0.5
(d) 1
Answer:
(a) 2
Hint:
C2H6 – Ethane – molar mass = 24 + 6 = 30 g
30 g of C2H6 contains = 1 mole.
∴ 60 g of C2H6 will contains = 2 x 1 = 2 moles.

Question 36.
Which of the following method is used to prevent rusting of iron?
(a) Galvanization
(b) Painting
(c) Chrome plating
(d) all the above
Answer:
(d) all the above

Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Question 37.
Which of the following is not a redox reaction?
(a) H2 + F2 → 2HF
(b) Cu + 4HNO3 → Cu(NO3)2 + 2NO2 + 2H2O
(c) 2H2 + O2 → 2H2O
(d) AgCl + NH3 → [Ag(NH3)2]Cl
Answer:
(d) AgCl + NH3 → [Ag(NH3)2]Cl

Question 38.
How many H2O molecules are there in a snowflake weighing 1 mg?
(a) 3.35 x 1019
(b) 6.023 x 1023
(c) 335 x 10-19
(d) 100
Answer:
(a) 3.35 x 1019
Hint:
1 mg of H2O
Molar mass of H2O = 2 + 16 = 18 g
1 Mole contains 6.023 x 1023 water molecules
18 g contains 6.023 x 1023 water molecules
l mg contains \(\frac{6.023 \times 10^{23}}{18}\) x 1g /1000 mg = 3.35 x 10-19 H2O molecule.

Question 39.
The volume of HCl gas weighing 73 g at STP is ……….
(a) 2.24 x 10-2 m3
(b) 4.48 x 10-2 m3
(c) 4.48 x 102m3
(d) 2.24 x 102m3
Answer:
(b) 4.48 x 10-2 m3
Hint:
HCl = Molar mass = 1 + 35.5 = 36.5 g
36.5 g of HCl occupies 2.24 x 10-2m3
∴ 73 g of HCl at STP will occupy \(\frac{2.24 \times 10^{-2}}{36.5}\) x 73 = 4.48 x 10-2m3

Question 40.
The molar volume of 22 g of CO2 is ……….
(a)2.24 x 10-2m3
(b)4.48 x 10-2m3
(c) 1.12 x 10-2m3
(d)2.24 x 10-2m3
Answer:
(c) 1.12 x 10-2m3
Hint:
CO2 = Molar’mass of 12 + 32 = 44 g
44 g of CO2 occupies molar volume = 2.24 x 10-2m3
∴ 2g of CO2 will occupy = \(\frac{2.24 \times 10^{-2}}{44}\) x 2= 1.12 x 10-2 L

Question 41.
The equivalent mass of Aluminium is ……….
(a) 27
(b) 13.5
(c) 54
(d) 9
Answer:
(d) 9

Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Question 42.
The equivalent mass of HSO4 is ……….
(a) 98
(b) 97
(c) 48
(d) 96
Answer:
(a) 98
Hint:
HSO4 = Molar mass= 1 + 32 + 64 + 1 = 98
Equivalent mass = Molar mass / 1 = 98

Question 43.
The equivalent mass of NaCl is ……….
(a) 40
(b) 58.5
(c) 35.5
(d) 23
Answer:
(b) 58.5
Hint:
NaCl = Salt Molar mass 23 + 35.5 = 58.5
Equivalent mass of Salt = Molar mass of Salt.

Question 44.
Match the List-I and List-lI using the correct code given below the list.
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
Answer:
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Question 45.
Match the List-I and List-Il using the correct code given below the list.
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
Answer:
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Question 46.
Consider the following statements ……….
(i) Empirical formula shows the actual number of atoms of different elements in one molecule of the compound.
(ii) Ozone is a diatomic molecule.
(iii) Gases are easily compressible.
Which of the above statement is/are not correct?
(a) (i), (ii), (iii)
(b) (i) & (ii)
(c) (ii) & (iii)
(d) (iii) only
Answer:
(b) (i) & (ii)

Question 47.
How many molecules of hydrogen is required to produce 4 moles of ammonia?
(a) 15 moles
(b) 20 moles
(c) 6 moles
(d) 4 moles
Answer:
(c) 6 moles
Hint:
3H2 + N2 → 2NH3
To get 2 moles of ammonia, 3 mole of H2 is required.
To get 4 moles of ammonia = \(\frac {3}{2}\), x 4
= 6 moles of H2 is required.

Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Question 48.
The number of moles of oxygen required to prepare 1 mole of water is …………..
(a) 1 mole
(b) 0.5 mole
(c) 2 moles
(d) 0.4 mole
Answer:
(b) 0.5 mole
Hint:
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations - 147
0.5 mole of oxygen is required to prepare 1 mole of H2O.

Question 49.
How much volume of CO2 is produced when 50 g of CaCO3 is heated strongly?
(a) 2.24 x 10-2 m3
(b) 22.4
(c) 11.2 L
(d) 22400 cm3
Answer:
(c) 11.2 L
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations - 148
100 g of CaCO3 produces 22.4 liters of CO2.
50 g of CaCO3 will produce = \(\frac{22.4}{100} \times 50\) = 11.2 litres

Question 50.
Which one of the following is not a redox reaction?
(a) Rusting of iron
(b) Extraction of metal Na
(c) Electroplating
(d) Aluminothermic process
Answer:
(a) Rusting of Iron

Question 51.
In the reaction 2 AuCl3 + 3 SnCl2 → 2 Au + 3 SnCl4 which is an oxidising agent?
(a) AuCl3
(b) Au
(c) SnCl2
(d) Both AuCl3 and SnCl2
Answer:
(a) AuCl3
Hint:
AuCl3 undergoes reduction. So, it is an oxidising agent.

Question 52.
Identify the compound formed during the rusting of iron.
(a) Fe2O3
(b) Fe2O3. x H2O
(c) FeO. x H2O
(d) FeO
Answer:
(b) Fe2O3. x H2O – Hydrated iron oxide is rust.

Question 53.
The oxidation state of a substance in its elementary state is equal to ………..
(a) -1
(b) -2
(c) zero
(d) charge of the ion
Answer:
(c) zero

Question 54.
The oxidation number of fluorine in all its compounds is equal to ………….
(a) -1
(b) +1
(c) – 2
(d) +2
Answer:
(a) -1

Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Question 55.
Consider the following statements.
(i) The sum of the oxidation number of all the atoms in a neutral molecule is equal to zero.
(ii) Fluorine has an oxidation number +1 in all its compounds.
(iii) The oxidation number of a substance in its elementary state is equal to zero.
Which of the above statement is/are not correct?
(a) (i), (ii) & (iii)
(b) (ii) & (iii)
(c) (i) only
(d) (ii) only
Answer:
(d) (ii) only

Question 56.
The oxidation number of Cr in K2Cr2O7 is ………….
(a) +4
(b) + 6
(c)  O
(d) + 7
Answer:
(b) + 6
K2Cr2O2
2 + 2x – 14 = 0
2x – 12 = 0
2x = + 12
x = + 6

Question 57.
The oxidation number of N in NH4 ion is ……….
(a) +4
(b) + 3
(c) – 3
(d) – 4
Answer:
(c) – 3
NH2+
x + 4 = + 1
x = + 1 – 4
x = – 3

Question 58.
Zn(s) + Cu2+(aq) → Zn2+(aq) + Cu(s). In this reaction, which gets oxidised?
(a) Cu2+
(b) Zn2+
(c) Zn
(d) Zn, Cu2+
Answer:
(c) Zn
Hint:
Zn → Zn2+ + 2e (loss of electron = oxidation)
Zn gets oxidised

Question 59.
Which one of the following is an example of disproportionation reaction?
(a) CuSO4 + Zn → ZnSO4 + Cu
(b) 2KClO3 → 2KCI + 3O2
(c) PCl5 → PCl3 + Cl2
(d) 4H3PO3 → 3H3PO4 + PH3
Answer:
(d) 4H3PO3 → 3H3PO4 + PH3 (Auto oxidation and reduction reaction)

Question 60.
The number of molecules in 40 g of sodium hydroxide is ……….
(a) 6.023 x 1023
(b) 3.0115 x 1023
(c) 6.023 x 1023
(d) 2 x 6.023 x 1023
Answer:
(c) 6.023 x 1023
Sodium hydroxide = NaOH = 23 + 16 + 1 = 40 g
40g = 1 mole = 6.023 1023

Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Question 61.
The mass of one molecule of AgCl in grams is ……….
(a) 108 g
(b) 143.5 g
(c) 35.5 g
(d) 243.5 g
Answer:
(b) 143.5 g
Hint:
Mass of AgCl = 108 + 35.5 = 143.5 g.

Question 62.
The empirical formula of Alkene is ……….
(a) CH
(b) CH2
(c) CH3
(d) CH3O
Answer:
(b) CH2
Hint:
Alkene CnH2n Molecular formula
E.F. = M.F./2
∴ Empirical formula = CH2

Question 63.
22 g of a gas occupies 11.2 liters of volume at STP. The gas is ……….
(a) CH4
(b) NO
(c) CO
(d) CO2
Answer:
(d) CO2
Hint:
22 g of a gas occupies 11.2 liters.
11.2 liters is occupied by 22 g of gas.
∴ Molar volume 22.4 liter will be occupied by \(\frac {22}{11.2}\) x 22.4 = 44 g
∴ The gas is CO2.

Question 64.
The number of moles of H2 in 2.24 liter of hydrogen gas at STP is ……….
(a) 1
(b) 0.1
(c) 0.01
(d) 0.001
Answer:
(b) 0.1
Hint:
22.4 liter = 1 molar volume = 1 mole.
∴ 2.24 liter = \(\frac {1}{22.4}\) x 2.24 = 01 mole

Question 65.
How many molecules are present in 32 g of methane?
(a) 2 x 6.023 x 1023
(b) 6.023 x 1023
(c) 6.023 x 1023
(d) 3.011 x 1023
Answer:
(a) 2 x 6.023 x 1023
Hint:
Methane (CH4) – Molar mass = 12 + 4 = 16g.
16 g contains 6.023 x 1023 molecules.
∴ 32 g of methane will contain = \(\frac{6.023 \times 10^{23}}{16} \times 32^{2}\) = 2 x 6.023 x 1023

Question 66.
The empirical formula of glucose is ……….
(a) CH
(b) CH2O
(c) CH2O2
(d) CHO
Answer:
(b) CH2O
Hint:
Glucose = Molecular formula = C6H12O6
Empirical formula = \(\frac { Molecular formula}{6}\) = \(\\frac{\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}}{6}\) = CH2O

Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Question 67.
How many moles of water is present in I L of water?
(a) 1
(b) 18
(c) 55.55
(d) 5.555
Answer:
(c) 55.55
Hint:
1 Liter of water = 1000 g.
The molar mass of water = 18 g
Number of moles = \(\frac {Mass}{Molar mass}\) = \(\frac {1000}{18}\) = 55.55 moles

Question 68.
How many moles of hydrogen atoms are present in 1 mole of C2H6?
(a) 18 moles
(b) 6 moles
(c) 3 moles
(d) 1 mole
Answer:
(b) 6 moles
Hint:
C2H6 contains 6H atoms. 6 moles.

Question 69.
The molar mass of Na2SO4 is ……….
(a).129
(b) 142
(c) 110
(d) 70
Answer:
(b) 142
Hint:
Na2 SO4 = Molar mass
= (23 x 2) + (32 x 1) + (16 x 4)
= 46 + 32 + 64
= 142

Question 70.
Match the List-I with List-Il using the correct code given below the list.
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
Answer:
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Question 71.
Ore mole of CO2 contains ………….
(a) 6.02 x 1023 atoms of C
(b) 3 g of CO2
(c) 6.02 1023 atoms of O
(d) 18.1 x 1023 molecules of CO2
Answer:
(a) 6.02 x 1023 atoms of C

Question 72.
5.6 liters of oxygen at STP is equivalent to ……….
(a) 1 mole
(b) 1/4 mole
(c) 1/8 mole
(d) 1/2 mole
Answer:
(b) 1/4 mole
Hint:
22.4 litres of O2 = 1 mole
∴ 5.6 litres of O2 = \(\frac {1}{22.4}\) x 5.6 = 0.25 mole = 1/4 mole.

Question 73.
How many grams are contained in 1 gram atom of Na?
(a) 13 g
(b) 1 g
(c) 23 g
(d) 1/23 g
Answer:
(c) 23 g
Hint:
1 gram atom of Na
Na = Atomic mass 23 g (or) 23 amu
1 gram atom of Na = 1 mole = 23 g.

Question 74.
12 g of Mg will react completely with an acid to give ……….
(a) 1 mole of O2
(b) 1/2 mole of H2
(c) 1 mole of H2
(d) 2 mole of H2
Answer:
(b) 1/2 mole of H2
Hint:
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
∴ 12 g of Mg \(\frac {1}{2}\) mole of H2O

Question 75.
which of the following has the highest mass?
(a) I g atom of C
(b) 1/2 mole of CH4
(c) 10 ml of water
(d) 3.011 x 1023 atoms of oxygen
Answer:
(a) I g atom of C
(a) 1 g atom of C = 12 g
(b) 1/2 mole of CH4 = \(\frac {12 + 4}{2}\) = 8 g.
(c) 10 ml of water (H2O) = 1 x 10 = 10 g
(d) 3.011 x 1023 atoms of oxygen = 0.5 mole of oxygen = 8 g

Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Question 76.
The empirical formula of sucrose is ……….
(a) CH2O
(b) CHO
(c) C12H22O11
(d) C(H2O)2
Answer:
(a) CH2O
Hint:
Sucrose Molecular formula = C12H22O11
E.F.= \(\frac{\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}}{12}\) = CH2O

Question 77.
The number of grams of oxygen in 0.10 mol of Na2CO3. 10H2O is ………..
(a) 20.8 g
(b) 18 g
(c) 108 g
(d) 13 g
Answer:
(a) 20.8 g
Hint:
Na2CO2.10H2O = 1 mole
1 mole of Na2CO3. 10H2O contains 13 oxygen atoms.
Mass of 13 oxygen atoms = 13 x 16 = 208
1 mole of Na2CO3.10H2O contains 208 g of oxygen.
∴ 0.10 mole of Na2CO3.10H2O contains \(\frac {208}{1}\) x 0.12 = 08 g.

Question 78.
The mass of an atom of nitrogen is ……….
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
Answer:
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Question 79.
Which of the following halogens do not exhibit positive oxidation numbers in their compounds?
(a) Fluorine
(b) Chlorine
(c) Iodine
(d) Bromine
Answer:
(a) Fluorine

Question 80.
Which of the following is the most powerful oxidizing agent?
(a) KMnO4
(b) K2Cr2O7
(c) O3
(d) H2O2
Answer:
(a) KMnO4

Question 81.
On the reaction 2Ag + H2SO4 → Ag2SO4 + 2H2O + SO2. Sulphuric acid acts as ……………
(a) oxidizing agent
(b) reducing agent
(c) a catalyst
(d) an acid as well as an oxidant
Answer:
(d) an acid as well as an oxidant

Question 82.
The oxidation number of carboxylic carbon atom in CH3COOH is ……….
(a) + 2
(b) + 4
(c) + 1
(d) + 3
Answer:
(d) + 3
CH3COOH
-3 + 3 + x – 4 + 1
x – 3 = 0
x = + 3
Carboxylic carbon oxidation number = + 3

Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Question 83.
When methane is burnt in oxygen to produce CO2 and H2O, the oxidation number of carbon changes by ……….
(a) – 8
(b) + 4
(c) zero
(d) + 8
Answer:
(b) + 4
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Question 84.
The oxidation number of carbon is zero in ……….
(a) HCHO
(b) C12H22O11
(c) C6H12O6
(d) all the above
Answer:
(d) all the above

Question 85.
The oxidation number of Fe in Fe2(SO4)3 is ……….
(a) + 2
(b) + 3
(c) + 2, + 3
(d) O
Answer:
(b) + 3
Fe2(SO4)3
2x – 6 = 0
x = + 3

Question 86.
Among the following molecules in which Chlorine shows maximum oxidation state?
(a) Cl21
(b) KCl
(c) KClO3
(d) Cl2O7
Answer:
(d) Cl2O7
Cl2O7
2x – 14 = 0
2x = + 14
x = + 7

Question 87.
The oxidation number of carbon in CH3 → CH2OH is ………….
(a) + 2
(b) – 2
(e) O
(d) + 4
Answer:
(b) – 2
C2H5OH
2x +6 – 2 = O
2x + 4 = 0
2x = -4
x = -2

Samacheer Kalvi 11th Chemistry Basic Concepts of Chemistry and Chemical Calculations 2 – Mark Questions

I. Write brief answer to the following questions:

Question 1.
Define a matter.
Answer:
The matter is defined as anything that has mass and occupies space. All matter is composed of atoms.

Question 2.
What is molar volume?
Answer:
Molar volume is the volume occupied by one mole of a substance in the gaseous state at STP. It is equal to 2.24 x 10-2m3 (22.4 L).

Question 3.
The approximate production of Na2CO3 per month is 424 x 106 g while that of methyl alcohol is 320 x 106 g. Which is produced more in terms of moles?
Answer:
Na2CO3 mass = 424 x 106g
Molecular mass of Na2CO3 = (23 x 2) + 12 + (16 x 3)
= 46+ 12 +48
= 106 g
No. of moles of Na2CO3 Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
= 4 x 106 moles
Methyl alcohol mass = 320 x 106 g
Molecular mass of CH3OH = 12 + (1 x 4)+ 16 = 32 g
= 12 + 4 + 16 = 32 g
No. of moles of Methyl alcohol Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
= 10 x 106 moles.
∴ Methyl alcohol is more produced in terms of moles.

Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Question 4.
What is a mixture? Give an example.
Answer:
Mixtures consist of more than one chemical entity present without any chemical interactions. They can be further classified as homogeneous or heterogeneous mixtures based on their physical appearance.
Example: Air

Question 5.
Find the molecular mass of FeSO4.7H2O
Answer:
Sum of Atomic mass of all elements = Molecular mass
Atomic mass of Fe = 56.0
Atomic mass of S = 32.0
Atomic mass of 4[O] = 64.0
Atomic mass of 14[H] = 14.0
Atomic mass of 7[O] = 112.0 = 278.0
Molecular mass of FeSO4.7H2O = 278 g.

Question 6.
What is an element? Give examples.
Answer:
An element consists of only one type of atom. The element can exist as monoatomic or polyatomic units. The polyatomic elements are called molecules.
Example: Gold (Au), Hydrogen (H2).

Question 7.
How many moles of glucose are present in 720 g of glucose?
Answer:
Glucose = C6H4O4
Molecular mass of Glucose = (12 x 6) + (1 x 12) + (16 x 6)
= 72 + 12 + 96 = 180
\(\frac {720}{180}\) = 4 moles.

Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Question 8.
Define atomic mass unit (AMU).
Answer:
The AMU or unified atomic mass is defined as one-twelfth of the mass of a Carbon – 12 atoms in its ground state.
i.e., 1 amu (or) 1 u ≈ 1.6605 X 10-27 kg

Question 9.
What do you understand by the terms acidity and basicity?
Answer:
Acidity: The number of hydroxyl ions present in one mole of a base is known as the acidity of the base.
Basicity: The number of replaceable hydrogen atoms present in a molecule of acid is referred to as its basicity.

Question 10.
Calculate the equivalent mass of bicarbonate ion.
Answer:
Bicarbonate ion = HCO3
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
Formula mass of HCO3 = 1 + 12 + 48 = 61
Equivalent mass of HCO3 = \(\frac {61}{1}\) = 61

Question 11.
What is relative molecular mass?
Answer:
Relative molecular mass is defined as the ratio of the mass of a molecule to the unified atomic mass unit.

Question 12.
Calculate the equivalent mass of hydrated sodium carbonate.
Answer:
Hydrated sodium carbonate = Na2CO3. 10H2O
Molecular mass of Na2CO3. 10H2O = (23 x 2) + (2 x 1) + (16 x 13) + (1 x 20)
= 46 + 12 + 208 + 20 = 286
Equivalent mass of Na2CO3. 10H2O = \(\frac {Molecular mass}{Acidity}\)
= \(\frac {286}{2}\) = 143

Question 13.
What are antacids?
Answer:
Antacids are commonly used medicines for treating heartburn and acidity. Antacids contain mostly magnesium hydroxide or aluminium hydroxide that neutralizes the excess acid.

Question 14.
Boric acid, H3BO3 is a mild antiseptic and is often used as an eyewash. A sample contains 0.543 mol H3BO3. What is the mass of boric acid in the sample?
Answer:
Molecular mass of H3BO3 = (1 x 3) + (11 x 1) + (16 x 3) = 62
The boric acid sample contains 0.543 moles.
Mass of 0.543 mole of Boric acid = Molecular mass x mole
= 62 x 0.543
= 33.66 g

Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Question 15.
A compound contains 50% of X (atomic mass 10) and 50% Y (atomic mass 20). Give its molecular formula
Answer:
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
∴ The Empirical Formula is X3Y
Empirical Formula mass = 20 + 20 = 40
Molecular mass = Sum of atomic mass = 40
n = 1, Molecular formula = (Empirical Formula )n = (X2Y)1 = X2Y.

Question 16.
Define molar mass.
Answer:
Molar mass is defined as the mass of one mole of a substance. The molar mass of a compound is equal to the sum of the relative atomic masses of its constituents expressed in g mol-1.

Question 17.
Define matter. What are the types of matter?
Answer:

  • A matter is anything which has mass and occupies space.
  • Matters exist in all three states such as solid, liquid, and gas.

Question 18.
Prove that states of matter are interconvertible.
Answer:
States of matter are interconvertible by changing temperature and pressure.
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Question 19.
What is the basicity of an acid? Give an example.
Answer:
Basicity of an acid is the number of moles of ionizable H+ ions present in 1 mole of the acid. The basicity of sulphuric acid (H2SO4) is 2.

Question 20.
Differentiate an element and an atom.
Answer:

  • An atom is the ultimate smallest electrically neutral, being made up of fundamental particles such as the proton, neutron, and electron.
  • An element consists of only one type of atom. Elements are further divided into metals, non-metals, and metalloids.

Question 21.
Distinguish between a molecule and a compound
Answer:
Molecule:

  • A molecule is the smallest particle made up of one or more than one atom in a definite ratio having stable and independent existence.
  • e.g. Na – Monoatomic molecule O2 – Diatomic molecule P4 – Poly atomic molecule

Compound:

  • A molecule which contains two or more atoms of different elements are called a compound molecule.
  • e.g. CO2 – Carbon dioxide CH4 – Methane H2O – Water

Question 22.
What is the molecular formula of a compound?
Answer:
The molecular formula of a compound is the formula written with the actual number of different atoms present in one molecule as a subscript to the atomic symbol.

Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Question 23.
Define the molecular mass of a substance.
Answer:
Molecular mass of a substance (element or compound) represents the number of times the molecule of that substance is heavier than 1 / 12th of the mass of an atom of C-12 isotope. Molecular mass = 2 x Vapour density

Question 24.
Calculate the molecular mass of Sulphuric acid (H2SO4). Element
Answer:
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Question 25.
What are redox reactions?
Answer:
The reaction involving loss of electron is oxidation and gain of the electron is reduced. Both these reactions take place simultaneously and are called as redox reactions.

Question 26.
Calculate the number of moles present in 60 g of ethane.
Answer:
No. of moles =Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations  = \(\frac {W}{M}\)
Molar Mass of ethane (C2H6) = 24 + 6 = 30
Number of moles in 60 g of ethane = \(\frac {60}{30}\) = 2 moles.

Question 27.
Define oxidation and reduction in terms of oxidation number.
Answer:
A reaction in which the oxidation number of the element increases is called oxidation whereas the reaction in which oxidation number decreases is called reduction.

Question 28.
Calculate the equivalent mass of (i) Sulphate ion (ii) Phosphate ion.
Answer:
(i) Sulphate ion (SO42-).
Equivalent mass of Sulphate = Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations = \(\frac {32 + 64}{2}\) = \(\frac {96}{2}\) = 48 g eq-1

(ii) Phosphate ion (P043-)
Molar mass of Phosphate ion = Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations = \(\frac {31 + 64}{3}\) = \(\frac {95}{2}\) = 31.6 = 31.6g eq-1

Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Question 29.
Calculate the equivalent mass of sulphuric acid.
Answer:
Sulphuric acid = H2SO4
Molar mass of Sulphuric acid = 2 + 32 + 64 = 96
Basicity of Sulphuric acid = 2
Equivalent mass of acid = Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations = \(\frac {96}{2}\) = 49g eq-1

Question 30.
How many moles of hydrogen is required to produce 20 moles of ammonia?
Answer:
3H2 + N2 → 2NH3
A per stoichiometric equation,
No. of moles of hydrogen required for 2 moles of ammonia 3 moles
No. of moles of hydrogen required for 20 moles of ammonia = \(\frac {3}{2}\) x 20 = 30 moles.

Question 31.
Calculate the amount of water produced by the combustion of 32 g of methane.
Answer:
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
As per the stoichiometric equation,
16 g of methane produces 36 g of H2O
∴ 32 g of methane will produce = \(\frac {36}{16}\) x 32 = 72 g of water.

Question 32.
How much volume of Carbon dioxide is produced when 25 g of calcium carbonate is heated completely under standard conditions?
Answer:
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
100 g of CaCO3 produces 22.4 L of CO2.
∴ 25 g of CaCO3 will produce = \(\frac {22.4}{100}\) x 25 = 5.6 L of CO2.

Question 33.
How much volume of chlorine is required to prepare 89.6 L of HCl gas at STP?
Answer:
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
2 x 22.4 L of HCl is produced by 22.4 L of Cl2.
∴ 89.6 L of HCl will be produced by = img = 89.6 L = 44.8 L of chlorine.

Question 34.
What is meant by limiting reagent?
Answer:
A large excess of one reactant is supplied to ensure the more expensive reactant is completely converted to the desired product. The reactant used up first in a reaction is called the limiting reagent.

Question 35.
On the formation of SF6 by the direct combination of S and F2, which is the limiting reagent? Prove it.
Answer:
SF6 is formed by burning Sulphur in an atmosphere of Fluorine. Suppose 3 moles of S is allowed to react with 12 moles of Fluorine.
S(l) +3F2(g) → SF6(g)
As per the stoichiometric reaction, one mole of S reacts with 3 moles of fluorine to complete the reaction. Similarly, 3 moles of S requires only 9 moles of fluorine.
∴ It is understood that the limiting reagent is Sulphur and the excess reagent is Fluorine.

Question 36.
Mention any 4 redox reaction that takes place in our daily life.
Answer:

  1. Burning of cooking gas, wood
  2. Rusting of iron articles
  3. Electroplating
  4. Galvanic and electrolytic cells

Question 37.
Calculate the oxidation number of underlined elements in the following.

  1. KMnO4
  2. Cr2O72-

Answer:
1. KMnO4
1(+1) + x + 4 (-2) = 0
x – 7 = 0
∴ x = + 7
Oxidation state of Mn = +7.

2. Cr2O72-
2x + 7(-2) = -2
2x – 14 = – 2
2x = +l2
∴ x = + 6
Oxidation state of Cr = +6.

Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Question 38.
If 10 volumes of H2 gas react with 5 volumes of O2 gas, how many volumes of water vapour would be produced?
Answer:
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
Thus 2 volumes of H2 reacts with 1 volume of O2 to produce 2 volumes of H2O(g).
10 volumes of H2 would react with 5 volumes of O2 to produce 10 volumes of H2O(g)
Thus 10 volumes of H2O will be produced.

Question 39.
Which one of the following will have the largest number of atoms?

  1. 1 g of Au(s)
  2. 1 g of Na(s)
  3. 1 g of Li(s)
  4. 1 g of Cl2 (g)

Answer:
1. Molar mass of Au = 197 g mol-1.
No: of atoms in 1 g of Au = \(\frac {1}{197}\) x 6.023 x 1023

2. Molar mass of Na = 23 g mol-1.
No of atoms in 1 g of Na = \(\frac {1}{23}\) x 6.023 x 1023

3. Molar mass of Li = 7 g mol-1
No. of atoms in 1 g of Li = \(\frac {1}{7}\) x 6.023 x 1023

4.  Molar mass of Cl2 = 35.5 g mol-1
No. of atoms in 1 g of Cl2 = \(\frac {1}{35.5}\) x 6.023 x 1023

Comparing the number of atoms, the largest number of atoms will be present in 1 g of Li. Since the mass is same in each case, the element with the lowest molar mass would have the largest number of atoms.
∴ Li with lowest molar mass would have the largest number of atoms.

Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Question 40.
Calculate the relative molecular mass of glucose. (Given: Atomic mass of C =12, H = 1.008 and O = 16).
Answer:
Relative molecular mass of glucose (C6H12O6)
= (6 × 12) + (12 × 1.008) + (6 × 16)
= 72 + 12.096 + 96
= 180.096.

Question 41.
Justify the following reaction is a redox reaction.
Answer:
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
In the above reaction, oxygen is removed from CuO. So CuO gets reduced. Oxygen is added to H2 to form water. So H2 gets oxidised. i.e. In CuO, oxidation number of Cu +2 is reduced to O whereas in H2, oxidation of H2 O is increased to + 1. So the above reaction is a redox reaction.

Samacheer Kalvi 11th Chemistry Basic Concepts of Chemistry and Chemical Calculations 3 – Mark Questions

Question 1.
Distinguish among the different physical states of matter.
Answer:
Differences among three physical states of matter (solid, liquid and gas) are as follows

S.No. Properties Solid Liquid Gas
1. Volume Definite Definite No definite
2. Shape Definite No definite No definite
3. Molecular arrangement Very closely packed Loosely packed Very loosely packed
4. Freedom of movement Not much freedom Move around and better than solid Move easy and fast
5. Compressibility Non-compressible Less compressible Easily compressible

Question 2.
Define equivalent mass of salt.
Answer:
Equivalent mass of a salt:
It is defined as the number of parts by mass of the salt that is produced by the neutralization of one equivalent of an acid by a base. Therefore the equivalent mass of the salt is equal to its molar mass.

Question 3.
Describe the concept of stoichiometry.
Answer:
Stoichiometry gives the numerical relationship between chemical quantities in a balanced chemical equation. By applying the concept of stoichiometry, we can calculate the number of reactants required to prepare a specific amount of a product and vice versa using a balanced chemical equation.
Consider the following chemical reaction.
C(s) + O2(g) → CO2(g)
From this equation, we learned that 1 mole of carbon reacts with 1 mole of an oxygen molecule to form 1 mole of carbon dioxide.
1 mole of C ≡ 1 mole of O2 ≡ 1 mole of CO2
The symbol ‘≡’ means ‘stoichiometrically equal to’.

Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Question 4.
Calculate the equivalent mass of hydrated ferrous sulphate.
Answer:
Hydrated ferrous sulphate = FeSO4.7H2O
Ferrous sulphate – Reducing agent
Ferrous sulphate reacts with an oxidising agent in acid medium according to the equation.
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
16 parts by mass of oxygen oxidised 304 g of FeSO4.
8 parts by mass of oxygen will oxidise \(\frac{304}{16}\) x 8 parts by mass of FeSO4.
= 152
Equivalent mass of Ferrous sulphate (Anhydrous) = 152
Equivalent mass of crystalline Ferrous sulphate FeSO4 .7H2O = 152 + 126 = 278

Question 5.
Give differences between empirical and molecular formula
Answer:
Empirical Formula:

  • The empirical formula is the simplest formula.
  • It shows the ratio of a number of atoms of different elements in one molecule of the compound.
  • It is calculated from the percentage of composition of the various elements in one molecule.
  • For example, the Empirical formula of Benzene = CH.

Molecular Formula:

  • Molecular Formula is the actual formula.
  • It shows the actual number of different types of atoms present in one molecule of the compound.
  • It is calculated from the Empirical formula Molecular Formula = (Empirical formula)n
  • Molecular formula of Benzene = C6H6.

Question 6.
A sample of hydrated copper sulphate is heated to drive off the water of crystallization, cooled and reweighed 0.869 g of CuSO4 aH2O gave a residue of 0.556 g. Find the molecular formula of hydrated copper sulphate.
Answer:
0.869 g of CuSO4.aH2O gave a residue of 0.556 g of Anhydrous CuSO4.
∴ Weight of a H2O molecule = 0.869 – 0.556 = 0.313 g
Molecular weight of H2O = (1 x 2) + 16 = 2 + 16 = 18
No. of moles of water = \(\frac{Mass}{Molecular mass}\)
CuSO4.5H2O – Molecular mass = 63.5 + 32 + 64 + 90 = 249.5 g
249.5 g of CuSO4.5H2O on heating gives 159.5 g of CuSO4.
0.869 g of CuSO4.aH2O on heating gives = \(\frac{159.5}{249.5}\) x 0.869
= 0.556 g of anhydrous CuSO4 ∴ a = 5
The molecular formula of hydrated copper sulphate = CuSO4.5H2O

Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Question 7.
Balance by oxidation number method: Mg + HNO3 → Mg(NO3)2 + NO2 + H2O
Step – 1
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
Step – 2
Mg + 2HNO3 -» Mg(NO3)2 + NO2 + H2O
Step – 3
To balance the number of oxygen atoms and hydrogen atoms 2HNO3 is multiplied by 2.
Mg + 4HNO3 → Mg(NO3)2 + 2NO2 + H2O
Step – 4.
To balance the number of hydrogen atoms, the H2O molecule is multiplied by 2.
Mg + 4HNO3 → Mg(NO3)2 + 2NO2 + 2H2O

Question 8.
Explain about the classification of matter.
Answer:
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Question 9.
Calculate the mass of the following atoms in amu,
(a) Helium (mass of He = 6.641 x 10-24 g)
(b) Silver (mass of Ag = 1.790 x 10-22 g)
1 amu = 1.66056 x 10-24
Answer:
(a) The mass of Helium atom in amu = \(\frac{6.641 \times 10^{-24}}{1.66056 \times 10^{-24}}\) = 3.9992 amu.
(b) The mass of Silver atom in amu = \(\frac{1.790 \times 10^{-22}}{1.66056 \times 10^{-24}}\) = 107.79 amu.

Question 10.
Calculate the number of atoms present in 1 Kg of gold.
Answer:
The atomic mass of Gold = 197 g mol-1.
197 g of gold contains 6.023 x 1023 atoms of gold.
∴ 1000 g of gold will contain = \(\frac{1000 \times 6.023 \times 10^{23}}{197}\)
= 3.055 x 1024 atoms of Gold.

Question 11.
Calculate the molar volume of 146 g of HCl gas and the number of molecules present in it.
Answer:
Molar mass of HCl = 36.5 g
The molar volume of 36.5 g (1 mole) of HCl = 2.24 x 102 m3.
∴ The volume of 146 g (4 moles) of HCl = \(\frac{2.24 \times 10^{-2}}{36.5}\) x 146
= 8.96 x 10 m3
No. of molecules in 146 g of HCl = 4 N
= 4 x Avogadro Number
= 4 x 6.023 x 1023
= 24.092 x 1023
= 2.4092 x 1024 molecules.

Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Question 12.
Calculate the molar mass of 20 L of gas weighing 23.2 g at STP.
Molar mass =Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Molar volume at STP = 2.24 x 10-2 m3 = 22.4 L (or) 22400 cc.
Molar mass of the gas at STP = \(\frac{23.2 x 22.4}{20}\) = 25.984 g.

Question 13.
0.6 g of a metal gives on oxidation 1 g of its oxide. Calculate its equivalent mass.
Answer:
Mass of metal = 0.6
Mass of metal oxide = 1 g
Mass of oxygen = 1 – 0.6 = 0.4 g
0.4 g of oxygen combines with 0.6 g of metal.
∴ 8 g of oxygen will combine with = \(\frac{0.6}{0.4}\) x 8
Equivalent mass of the metal = 12 g eq-1.

Question 14.
How would you calculate the equivalent mass of anhydrous oxalic acid and hydrated oxalic acid.
Answer:
In acid medium,
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
16 g of oxygen is used for oxidation of 90 g of oxalic acid.
∴ 8 g of oxygen will oxidize = \(\frac{90}{16}\) x 8 = 45 g eq-1.
Equivalent mass of Anhydrous oxalic acid = 45 g eq-1
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
= \(\frac{126}{2}\) = 63 g eq-1.

Question 15.
A compound on decomposition in the laboratory produces 24.5 g of nitrogen and 70 g of oxygen. Calculate the empirical formula of the compound.
Answer:
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
the empirical formula is N2O5

Question 16.
What is the steps involve in the calculation of molecular formula from empirical formula?
Answer:
Molecular mass and empirical formula are used to deduce molecular formula of the compound.
Steps to calculate molecular formula:

  • if Empirical formula is found out from the percentage composition of elements
  • Empirical formula mass can be found from the empirical formula
  • Molecular mass is found out from the given data
  • Molecular formula = (Empirical formula)n
  • where, n = Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Question 17.
What is combination reaction? Give example.
When two or more substances combine to form a single substance, the reactions are called combination reactions.
A + B → C
Example:
2 Mg + O2 → 2MgO

Question 18.
What is decomposition reaction? Give two examples.
Answer:
Chemical reactions in which a compound splits up into two or more simpler substances are called decomposition reaction.
AB → A + B
Example:
2KCO3 → 2KCl + O2
PCl5 → PCl3 + Cl2

Question 19.
What is displacement reactions? Give its types. Explain with example.
Answer:
The reactions in which one ion or atom in a compound is replaced (or substituted) by an ion or atom of the other element are called displacement reactions.
AB + C → AC + B

Example:
Metal displacement
CuSO4 + Zn → ZnSO4 + Cu

Example:
Non-metal displacement
2KBr + Cl2 → 2KCl + Br2

Question 20.
What is disproportionation reactions? Give example.
Answer:
The reactions in which an element undergoes simultaneously both oxidation and reduction are called as disproportionation reactions.
Example:
P4 + 3NaOH + 3H2O → PH3 + 3NaH2PO2
2HCHO + H2O → CH3OH + HCOOH

Question 21.
What are competitive electron transfer reaction? Give example.
Answer:
These are the reactions in which redox reactions take place in different vessels and it is an indirect redox reaction. There is a competition for the release of electrons among different metals.
Example:
Zn releases electrons to Cu and Cu releases electrons to Silver and so on.
Zn(s) + Cu2+ → Zn2+(aq) + Cu(s) (Here Zn – oxidised; Cu2+ – reduced)
Cu(s) + 2Ag+ → Cu2+(aq) + 2Ag(s) (Here Cu – oxidised; Ag+ – reduced)

Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Question 22.
Balance the following equation using oxidation number method.
Answer:
1. S + HNO3 → H2SO4 + NO2 + H2O
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
2. S + 6HNO3 → H2SO4 + NO2 + H2O
3. Balance the equation (except O and H)
S + 6HNO3 → H2SO4 + 6NO2 + H2O
4. Balance O atoms by adding 2H2O
5 + 6HNO3 → H2SO4 + 6NO2 + 2H2O

Question 23.
Determine the empirical formula of an oxide of iron which has 69.9% iron and 30.1% oxygen by mass.
Answer:
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
the empirical formula is Fe2O3

Question 24.
In three moles of ethane (C2H6) calculate the following:

  1. Number of moles of carbon atoms.
  2. Number of moles of hydrogen atoms.
  3. Number of molecules of ethane.

Answer:

(1) 1 mole of C2H6 contains 2 moles of Carbon atoms.
∴ 3 moles of C2H6 will have 6 moles of Carbon atoms.
(2) 1 mole of C2H6 contains 6 moles of Hydrogen atoms.
∴ 3 moles of C2H6 will have 18 moles of Hydrogen atoms.
(3) 1 mole of C2H6 contains 6.023 x 1023 number of molecules.
∴ 3 moles of C2H6 will contain 3 x 6.023 x 1023molecules.

Question 25.
Chlorine is prepared in the laboratory by treating manganese dioxide (MnO2) with aqueous hydrochloric acid according to the reaction.
4HCl(aq) + MnO2(s) → 2H2O(l) + MnCl2(aq) + Cl2(aq)
How many grams of HCl react with 5.0 g of manganese dioxide? (Atomic mass of Mn = 55 g).
Answer:
1 mole of MnO2 = 55 + 32 = 87 g.
87 g of MnO2 reacts with 4 moles of HCl. i.e. = 4 x 36.5 = 146 g of HCl.
∴ 5 g of MnO2 will react with \(\frac{146}{87}\) x 5.0 = 8.40 g.

Question 26.
The density of water at room temperature is 1.0 g/ml. How many molecules are there in a drop of water if its volume is 0.05 ml?
Answer:
Volume of drop of water = 0.05 ml
Mass of a drop of water = Volume x Density
= 0.05 ml x 1.0 g / ml.
= 0.05 g
Molar mass of water (H2O) = 18 g
18 g of water = 1 mole
0. 05 g of water = \(\frac{1}{18}\) x 0.05 = 0.0028 mol.
No. of molecules present in one mole of water = 6.023 x 1023
No. of molecules present in 0.0028 mole of water = \(\frac{6.023 \times 10^{23} \times 0.0028}{1}\) = 1.68 x 1021 water molecules

Question 27.
Balance the following equation by oxidation number method. MnO4 + Fe2+ → Mn 2+ + Fe3+ (Acidic medium)
Answer:
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
MnO4 + 5e → Mn2+ ……….(1)
Fe2+ → Fe3+ + e ……….(2)
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
to balance O and H atoms H2O and H+ are added.
MnO4 + 5Fe2+ + 8H+ → 5Fe3+ + Mn2+ + 4H2O

Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Samacheer Kalvi 11th Chemistry Basic Concepts of Chemistry and Chemical Calculations 5-Mark Questions

I. Answer the following questions in detail
Question 1.
Define the following (a) equivalent mass of an acid (b) equivalent mass of a base (c) equivalent mass of an oxidising agent (cl) equivalent mass of a reducing agent.
Answer:
(a) Equivalent mass of an acid:
Equivalent mass of an acid is the number of parts by mass of the acid which contains 1.008 part by mass of replaceable hydrogen atom.
Equivalent mass of an acid = Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

(b) Equivalent mass of a base:
It is defined as the number of parts by mass of the base which contains one replaceable hydroxyl ion or which completely neutralizes one gram equivalent of an acid.
Equivalent mass of a base = Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

(c) Equivalent mass of an oxidising agent:
It is defined as the number of parts by mass of an oxidising agent which can furnish 8 parts by mass of oxygen for oxidation.

(d) Equivalent mass of a reducing agent:
It is defined as the number of parts by mass of the reducing agent which is completely oxidised by 8 parts by mass of oxygen or with one equivalent of any oxidising agent.

Question 2.
Find the oxidation number of the following:
(i) S in H2SO4
⇒ 2(+1) + x + 4(-2) = 0
⇒ 2 + x – 8 = 0
⇒ x = +6
Oxidation number of S in sulphuric acid is +6.

(ii) Cr in Cr2O72-
⇒ 2x + 7(-2) =0
⇒ 2x – 14 = 0
⇒ x = + 7
Oxidation number of Cr in dicghromate ion is +7.

(iii) C in CH2F2
⇒ x + 2(+ 1) + 2(-1) = 0
⇒ x + 2 – 2 = 0
⇒ x = 0
Oxidation number of C in CH2F2 is 0.

(iv) S in SO2
⇒ x + 2(- 2) = 0
⇒ x – 4 = 0
⇒ x = + 4
Oxidation number of S in Sulphur dioxide is +4.

(v) O in OF2
⇒ x + 2(-1) = 0
⇒ x – 2 = 0
⇒ x = +2
Oxidation number of oxygen in OF2 is + 2

Question 3.
Determine the empirical formula of a compound containing K = 24.15%, Mn = 34.77% and rest is oxygen.
Answer:
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
empirical formula of a compound = KMnO4

Question 4.
Write the steps to be followed for writing empirical formula.
Answer:
Empirical formula shows the ratio of number of atoms of different elements in one molecule of the compound.
Steps for finding the Empirical formula:
The percentage of the elements in the compound is determined by suitable methods and from the data collected; the empirical formula is determined by the following steps.

  1. Divide the percentage of each element by its atomic mass. This will give the relative number of atoms of various elements present in the compound.
  2. Divide the atom value obtained in the above step by the smallest of them so as to get a simple ratio of atoms of various elements.
  3. Multiply the figures so obtained, by a suitable integer if necessary in order to obtain whole number ratio.
  4. Finally write down the symbols of the various elements side by side and put the above numbers as the subscripts to the lower right hand of each symbol. This will represent the empirical formula of the compound.
  5. Percentage of Oxygen = 100 – Sum of the percentage masses of all the given elements.

Question 5.
An organic compound was found to contain carbon = 40.65%, hydrogen = 8.55% and Nitrogen = 23.7%. Its vapour density was found to be 29.5. What is the molecular formula of the compound?
Answer:
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
Empirical formula = C2H5NO
Molecular mass = 2 x vapour density = 2 x 29.5 = 59.0
Empirical formula mass of C4H5NO = 24 + 5 + 14 + 16 = 59
n = Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations  = \(\frac {59}{59}\) = 1
Empirical formula mass 59
.’. Molecular formula = (Empirical formula)n
= (C2H5NO)1
Molecular formula = C2H5NO

Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Question 6.
Calculate the empirical and molecular formula of a compound containing 32% carbon, 4% hydrogen and rest oxygen. Its vapour density is 75.
Answer:
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
Empirical formula = C2H3O3
Empirical formula mass = 24 + 3 + 48 = 75
Molecular mass = 2 x Vapour density = 2 x 75 = 150
n = Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations  = \(\frac {150}{75}\) = 2
Molecular formula = (Empirical formula)n
Molecular formula = C2H3O3 x 2
Molecular formula = C4H6O6

Question 7.
Explain the different types of redox reactions with example.
Answer:
Redox reactions are classified into the following types:
(1) Combination reactions:
When two or more substances combine to form a single substance, the reactions are called combination reactions.
Example:
2Mg + O2 → 2MgO

(2) Decomposition reactions:
Chemical reactions in which a compound splits up into two or more simpler substances are called decomposition reaction.
Example:
2KClO3 → 2KCl + 3O2

(3) Displacement reactions:
The reactions in which one ion or atom in a compound is replaced by an ion or atom of the other element are called displacement reactions.
Example:
CuSO4 + Zn → ZnSO4 + Cu

(4) Disproportionation reactions:
The reactions in which an element undergoes simultaneously both oxidation and reduction are called as disproportionation reactions.
Example:
2HCHO + H2O → CH3OH + HCOOH

(5) Competitive Electron transfer reactions:
These are the reactions in which redox reactions take place in different vessels and it is an indirect redox reaction. There is a competition for the release of electrons among different metals.
Example:
Zn(s) + Cu2+ → Zn2+(aq) + Cu(s)  Here Zn – oxidised; Cu2+ reduced

Question 8.
Write the steps to be followed while balancing redox equation by oxidation number method.
Answer:
Oxidation number method:
This method is based on the fact that
Number of electrons lost by atoms = Number of electrons gained by atoms

Steps to be followed while balancing Redox reactions by Oxidation Number method:

  1. Write skeleton equation representing redox reaction
  2. Write the oxidation number of atoms undergoing oxidation and reduction.
  3. Calculate the increase or decrease in oxidation numbers per atom.
  4. Make increase in oxidation number equal to decrease in oxidation number by multiplying the formula of oxidant and reductant by suitable numbers.
  5. Balance the equation atomically on both sides except O and H atoms.
  6. Balance oxygen atoms by adding required number of water molecules to the side deficient
    in oxygen atoms.
  7. Add required number of H+ ions to the side deficient in hydrogen atom if the reaction is in acidic medium.
  8. For reactions in basic medium, add H2O molecules to the side deficient in hydrogen atoms and simultaneously add equal number of OH ions on the other side of the equation.
  9. Finally balance the equation by cancelling common species present on both sides of the equation.

Question 9.
Balance the following equation by oxidation number method:
Answer:
K2Cr2O7 + KCl + H2SO4 → KHSO4 + CrO2Cl 2 + H2O
Step – 1
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
Step – 2
K2Cr2O7 + KCl + H2SO4 → KHSO4 + 2CrO2C2 + H2O

Step 3.
To balance Cl atom, KC1 is multiplied by 4
K2Cr2O7 + 4KCl + H2SO4 → 2CrO2Cl2 + KHSO2 + H2O

Step 4.
To balance K atom, KHSO4 is multiplied by 6.
K2Cr2O7 + 4KCl + H2SO4 → 2CrO2Cl2 + 6KHSO4+ H2O

Step 5.
To balance O and H atoms, HSO4 is multiplied by 6, H20 is multiplied by 3.
Answer:
K2Cr2O7 + 4KCl + 6H2SO4 → 2CrO2Cl2 + 6KHSO4 + 3H2O

(2) P + HNO3 → H3PO4 + NO2 + H2O
Step – 1
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
Step 2.
P + 5HNO3 → H3PO4 + 5NO2 + H2O

(3) CuO + NH3 → Cu + N2 + H2O
Step 1.
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
Step 2.
3CuO + 2NH3 → 3Cu + N2 + H2O

Step 3.
To balance O and N, water is multiplied by 3.
3CuO + 2NH3 → 3Cu + N2 + 3H2O

(4) Zn + HNO3 →Zn(N03)2 + NH4NO3 + H2O
Step – 1.
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
Step 2.
4Zn + HNO3 → 4Zn(NO3)3 + NH4NO2 + H2O

Step 3.
To balance N, HNO3 is multiplied by 10
4Zn + 10HNO3 → 4Zn(NO3)2 + NH4NO3 + H3O

Step 4.
To balance oxygen, H2O is multiplied by 3
4Zn + 10HNO3 → 4Zn(NO3)2 + NH4NO3 + 3H3O

Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Question 10.
Balance the following equation by ion-electron method In acidic medium.
Answer:
(i) S2O32- + I2 → S2O42- + SO2 + I
Oxidation half reaction:
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
Reduction half reaction:
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
To balance, SO2 is added on RHS of the equation.
S2O32- + I2 → S2O42- + 2I + SO2
To balance oxygen atom, S2O32- and SO2 is multiplied by 2.
2S2O32- + I2 → S2O42- + 2I – + 2SO2

(2) Sb3+ + MnO4 → Sb5+ + Mn2+
Oxidation half reaction:
Sb3+ → Sb5+ + 2e ……….(1)
Reduction half reaction:
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
In equation (2), H2O is added on L.HS to balance oxygen atom.
MnO2 + 5e → Mn2+ + 4H2O ………(3)
To balance Hydrogen atoms, H’ is added on RHS.
MnO4 + 5e + 8H+ → Mn2+ + 4H2O ………(4)
Equation (4) is multiplied by 2 and equation (I) is multiplied by 5 to equalise the electrons gained and electrons lost.
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

(3) MnO4 + I → MnO2 + I2
Oxidation half reaction:
2I + 2e → I ………..(1)
Reduction half reaction:
MnO4  → MnO2 + e ………..(2)                                    
Equation (1)is multiplied by 3
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
Equation (2)is multiplied by 2.
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
To balance oxygen and hydrogen atoms, H+ is added on RHS and H2O is added on LHS.
2MnO4 + 6I + 4H+ → 2MnO2 + 2I2 + 2H2O

In acidic medium
(4) MnO4 + Fe2+ → Mn2+ + Fe3+
Oxidation half reaction:
Fe2+ → Fe3+ + e ……..(1)
Reduction half reaction:
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
To balance oxygen, H+ is added on RHS and H2O is added on LHS.
MnO4 + 5Fe2+ + 8H+ → Mn2+ + 5Fe3+ + 4H2O

(5) Cr(OH)4 + H2O2 → CrO4
Oxidation half reaction:
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
Reduction half reaction:
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
To balance oxygen and hydrogen atoms, OH and H2O are added.
2Cr(OH)4 + 3H2O2 + 20H → 2CrO2 + 8H2O

Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Question 11.
(a) Define equivalent mass of an oxidising agent.
(b) How would you calculate the equivalent mass of potassium permanganate?
(a) The equivalent mass of an oxidizing agent is the number of parts by mass which can furnish 8 parts by mass of oxygen for oxidation.
(b) Potassium permanganate is an oxidizing agent.
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
80 parts by mass of oxygen are given by 316 g of KMnO4.
.’. 8 parts by mass of oxygen will be furnished by \(\frac {316}{80}\) x 8 = 31.6
Equivalent mass of KMnO4 = 31.6 g eq-1.

Question 12.
(a) Define equivalent mass of an reducing agent.
(b) How would you determine the equivalent mass of Ferrous sulphate?
Answer:
(a) The equivalent mass of a reducing agent is the number of parts by mass of the reducing agent which is completely oxidised by 8 parts by mass of oxygen or one equivalent of any oxidising agent.
(b) Ferrous sulphate is a reducing agent.
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
16 parts by mass of oxygen oxidised 304 parts by mass of FeSO4.
∴ 8 parts by mass of oxygen will oxidise \(\frac {316}{80}\) x 8 parts by mass of ferrous sulphate = 152 .
The equivalent mass of ferrous sulphate (anhydrous) = 152.
The equivalent mass of crystalline ferrous sulphate is (FeSO4.7H2O) = 152 + 126 = 278
The equivalent mass of crystalline ferrous sulphate = 278.

Question 13.
A compound on analysis gave the following percentage composition: C = 24.47%, H = 4.07 %, Cl = 7 1.65%. Find out its empirical formula.
Answer:
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
the empirical formula is CH2Cl.

Question 14.
A laboratory analysis of an organic compound gives the following mass percentage composition: C = 60%, H = 4.48% and remaining oxygen.
Answer:
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
∴ the empirical formula is C9H8O4.

Question 15.
An insecticide has the following percentage composition by mass: 47.5% C, 2.54% H, and 50.0% Cl. Determine its empirical formula and molecular formulae. Molar mass of the substance is 354.5 g mol-1
Answer:
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
The empirical formula is C14H9C15.
Calculation of Molecular formula:
The empirical formula mass (C14H9C15) = (14 X 12) + (9 X 1) + (5 X 35.5)
n = Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations = \(\frac {354.5}{354.5}\) = 1
Empirical formula mass 354.5
Molecular formula = (Empirical formu1a)n
= (C14H9Cl5)1
∴ Molecular formula = C14H9Cl5

Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Question 16.
An organic fruit smelling compound on analysis has the following composition by mass: C = 54.54%, H = 9.09%, O = 36.36%. Find out the molecular formula of the compound. The vapour density of the compound was found to be 44.
Answer:
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
∴ The empirical formula is C2H4O
Theempirical formula mass(C2H4O) = (12 x 2)+(1 x 4)+(16 x 1) = 44
Molecular mass = 2 x Vapour density = 2 x 44 = 88
n = Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations = \(\frac {88}{44}\) = 2
Molecular formula = (Empirical formula)n
= (C2H4O)2
∴ Molecular formula = C2H4O2

Question 17.
Calculate the percentage composition of the elements present in magnesium carbonate. How many Kg of CO2 can be obtained from 100 Kg of is 90% pure magnesium carbonate.
Molar mass of MgCO3 = 84.32 g mol-1
Percentage of Mg = \(\frac {24}{84.32}\) x 100 = 28.46%
Percentage of C = \(\frac {12}{84.32}\) x 100 = 14.23%
Percentage of O3 = \(\frac {48}{84.32}\) x 100 = 57.0%
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
84.32 g of 100% pure MgCO3 gives 44g of CO2
∴ 100 x 103g of 100% pure MgCO3 gives = \(\frac {44}{84.32}\) x 100 x 103
= 52.182 x 103 g CO2
100% pure MgCO3 gives 52.182 x 103 g CO2
∴ 90% pure MgCO3 will give \(\frac{52.182 \times 10^{3}}{100}\) x 90 = 46963.8 g CO2

Question 18.
Urea is prepared by the reaction between ammonia and carbon dioxide.
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
In one process, 637.2 g of NH3 are allowed to react with 1142 g of CO2.
(a) Which of the two reactants is the limiting reagent?
(b) Calculate the mass of(NH4)2CO formed.
(c) how much of the excess reagent in grams is left at the end of the reaction?
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
No. of moles of ammonia = \(\frac{637.2}{17}\) = 37.45 mole
No. of moles of CO2 = \(\frac{1142}{44}\) = 25.95 moles
As per the balanced equation, one mole of CO2 requires 2 moles of ammonia.
∴ No. of moles of NH3 required to react with 25.95 moles of CO2 is = \(\frac {2}{1}\) x 25.95 = 51.90 moles.
∴ 37.45 moles of NH3 is not enough to completely react with CO2 (25.95 moles).
Hence, NH3 must be the limiting reagent, and CO2 is excess reagent.

(b) 2 moles of ammonia produce 1 mole of urea.
∴ Limiting reagent 37.45 moles of NH3 can produce \(\frac {1}{2}\) x 37.45 moles of urea.
= 18.725 moles of urea.
∴ The mass of 18.725 moles of urea = No. of moles x Molar mass
= 18.725 x 60
= 1123.5 g of urea.

(c) 2 moles of ammonia requires 1 mole of CO2.
∴ Limiting reagent 37.45 moles of NH3 will require x 37.45 moles of CO2.
= 18.725 moles of CO2.
∴ No. of moles of the excess reagent (CO2) left = 25.95 – 18.725 = 7.225
The mass of the excess reagent (CO2) left = 7.225 x 44 = 317.9 g CO2.

Question 19.
(a) Define oxidation number.
(b) What are the rules used to assign oxidation number?
Answer:
(a) Oxidation number refers to the number of charges an atom would have in a molecule or an ionic compound, if electrons were transferred completely.
(b) Rules to assign oxidation number:

  • Oxidation number of a substance in its elementary state is equal to zero (H2, Br2, Na)
  • Oxidation number of a mono-atomtic ion is equal to the charge on the Ton (Na4 =+ 1,
  • Oxidation number of hydrogen in a compound is +1 (except hydrides).
  • Oxidation number of hydrogen in metal hydrides is -1 (NaH, CaH2).
  • Oxidation number of oxygen in a compound is -2 (except OF2 and peroxides).
  • Oxidation number of oxygen in peroxides is -1 (He,, Na»,) = I.
  • Oxidation number of oxygen in fluorinated compounds is either +1 or +2.(OF2 = +2, O,F2 + 1).
  • Fluorine has an oxidation number -1 in all ìts compounds.
  • The sum of the oxidation number of all the atoms in neutral molecules is equal to Zero.
  • For all ions, the sum of the oxidation number of all atoms is equal to the charge of the ion.

Question 20.
Balance the following equation by oxidation number method.
C6H6 + O2 → CO2 + H2O
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
(ii) Balance the changes in O.N. by multiplying the oxidant and reductant by suitable numbers
2 C6H6 + 15 O2 → CO2 + H2O

(iii) Balance the equation atomically (except O and H).
2C6H6 + 15 O2 → 12 CO2 + H2O

(iv) Balance O atoms by adding one HzO molecule to the RHS for making the number of molecules of H2O to be 6.
2C6H6 + 15 O2 → 12 CO2 + 6H2O

Question 21.
Balance the following equation by oxidation number method.
KMnO4 + HCl → KCl + MnCl2 + H2O + Cl2
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

(ii) 2KMnO4 + 1OHCl → KCl + MnCl2 + H2O + Cl2

(iii) Balance the equation atomically (except O and H).
2KMnO4 + 1OHCl → 2KCl + 2MnCl2, + H2O + Cl2

(iv) Balance chlorine atoms by adding HC1 and multiplying Cl2 by 5.
2KMnO4 + 16HCl → 2KCl + 2MnCl2 + H2O + 5Cl2

(v) To balance O and H, H2O is multiplied by 8.
2KMnO4  + I6HCl → 2KCl + 2MnCl4 + 8H2O + 5Cl2

Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Question 22.
Balance the following equation by oxidation number method.
KMnO4 + FeSO4 + H2S04 → K2SO4 + MnSO4 + Fe2(S04)3 + H2O
Answer:
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
(ii) 2KMnO4 + 10FeSO4 + H2SO4 → K2SO4 + MnSO4 + Fe2(SO4)3+ H2O

(iii) Balance the equation atomically (except O and H) and sulphate ions.
2KMnO4 + 1OFeSO4 + 8H2SO4 → K2SO4 + 2MnSO4 + 5Fe4(SO4)3 + H2O

(iv) Balance O atoms by multiplying H2O by 8.
2KMnO4 + 1OFeSO4 + 8H2SO4 → K2SO4 + 2MnSO4 + 5Fe2(SO4)3 + 8H2O

Question 23.
Balancing of molecular equation in alkaline medium.
MnO2 + O2 + KOH → K2MnO4 + H2O
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

(ii) Balance the changes in O, N, by multiplying the oxidant and reductant by suitable numbers.
4MnO2 + 2O2+ KOH → K2MnO4 + H2O

(iii) Balance the equation atomically (except O and H).
4MnO2 + 2O2 + KOH → K2 MnO4 + H2O

(iv) Balance oxygen and hydrogen atoms by multiplying H20 by 4.
4MnO2 + 2O2 + 8KOH → 4K2MnO4 + 4H2O

Question 24.
Explain the steps involved in ion-electron method for balancing redox reaction.
Answer:
Ion electron method makes use of the Half reactions. Steps involved in this method are,

  1. Write the equation in the net ionic form without attempting to balance it.
  2. Write and locate the oxidation number of atoms undergoing oxidation and reduction from the knowledge of calculation of oxidation number.
  3. Write two half reactions showing oxidation and reduction separately.
  4. Balance oxygen atoms by adding required number of water molecules to the side deficient in oxygen atoms.
  5. Add required number of H+ ions to the side deficient in hydrogen atom if the reaction is in acidic medium
  6. Add electrons to whichever side is necessary to make up the difference in oxidation number.
  7. Add the two half reactions. The resulting equation is a net balanced equation.
  8. For reactions in basic medium, add H2O and hydrogen ion to balance H and O.
  9. Finally balance the equation by cancelling common species present on both sides of the equation.

Question 25.
Write balanced equation for the oxidation of Ferrous ions to Ferric ions by permanganate ions in acid solution. The permanganate ion forms Mn2+ ions under these conditions.
Answer:
Net ionic reaction:
MnO4 + Fe2+ + H+ → Mn2+ + Fe3+
Oxidation half reaction:
Fe2+ → Fe3+ + e ……….(1)
Reduction half reaction:
MnO4 + 5e → Mn2+ ……….(2)
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
To balance O and H, H+ and H2O are added.
MnO4 + 5Fe2+ + 8H+ → Mn2+ + 5Fe3+ +4H2O

Question 26.
A flask A contains 0.5 mole of oxygen gas. Another flask B contains 0.4 mole of ozone gas. Which of the two flasks contains greater number of oxygen atoms.
Answer:
Flask A:
1 mole of oxygen gas = 6.023 x 1023 molecules
∴ 0.5 mole of oxygen gas = 6.023 x 1023 x 0.5 molecules
The number of atoms in flask A = 6.023 x 1023 x 0.5 x 2 = 6.023 x 1023 atoms.

Flask B:
1 mole of ozone gas = 6.023 x 1023 molecules
0. 4 mole of ozone gas = 6.023 x 1023 x 0.4 molecules
The number of atoms in flask B = 6.023 x 1023 x 0.4 x 3 = 7.227 x 1023 atoms.
∴ Flask B contains a great number of oxygen atoms as compared to flask A.

Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

Question 27.
(a) Formulate possible compounds of ‘Cl’ in its oxidation state is:
0, – 1, + l, + 3,+ 5, + 7

(b) H2O2 act as an oxidising agent as well as reducing agent where as O3 act as only oxidizing agent. Prove it.
(a) (1) Cl oxidation number O in Cl2.
(2) Cl oxidation number -1 in HCl.
(3) Cl oxidation number +3 in HCl O2.
(4) Cl oxidation number +5 in KClO3.
(5) Cl oxidation number +7 in C12O7.

(b) In H2O2, oxidation number of oxygen is -1 and it can vary from O to -2 (+ 2 is possible in OF2). The oxidation number can decrease or increase, because of this H2O2 can act both oxidising and reducing agent. Ozone (O3 ) only acts as oxidising agent since it decomposes to give nascent oxygen.

Question 28.
The Mn3+ ion is unstable in solution and undergoes disproportionation to give Mn2+, MnO2 and H ion. Write a balanced ionic equation for the reaction.
The skeletal equation is:
Mn3+(aq) → Mn2+(aq) + MnO2(aq) + H+(aq)
Oxidation half equation:
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
Balance O.N. by adding electrons,
Mn3+(aq) →  MnO2(s) + e
Balance charge by adding 4H ions,
Mn3+(aq) →  MnO2(s) + 4H+(aq) + e
Balance O atoms by adding 2H2O
Mn3+(aq) + 22H2O(l) → MnO2(s) + 4H+(aq) + e ……….(1)
Reduction half equation:
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
Balance ON. by adding electrons:
Mn3+(aq) + e → Mn2+(aq) …………(2)
Adding Equation (1) and (2), the balanced equation for the disproportionation reaction is
2MH3+(aq) + 2H2O(l) → MnO2(s) + Mn2+(aq) + H+(aq)

Question 29.
Chlorine is used to purify drinking water. Excess of chlorine is harmful. The excess chlorine is removed by treating with sulphur dioxide. Present a balanced equation for the reaction for this redox change taking place in water.
The skeletal equation is:
Cl2(aq) + SO2(aq) + H2O(l) → Cl(aq) + SO42-(aq)
Reduction half equation:
Cl2(aq) → Cl2-(aq)
Balance Cl atoms,
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
Balance O.N. by adding electrons
Cl2(aq) + 2e → 2Cl + 2e
Oxidation half equation:
Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations
Balance O,N. by adding electrons
SO2(aq) → SO42-(aq) + 2e
Balance charge by adding 4H+ ions:
SO2(aq) → SO42-(aq) + 4H+(aq) + 2e
Balance O atoms by adding 2H2O
SO2(aq) + 2H2O(l) → SO42-(aq) + 4H+(aq) + 2e
Adding equation (1) and (2), we have,
Cl2(aq) + SO2(aq) + 2H2O(l) → Cl2(aq) + SO42-(aq) + 4H+(aq)
This represents the balanced redox reaction.

Samacheer Kalvi 11th Chemistry Solutions Chapter 1 Basic Concepts of Chemistry and Chemical Calculations

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Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State

Students can Download Chemistry Chapter 6 Gaseous State Questions and Answers, Notes Pdf, Samacheer Kalvi 11th Chemistry Solutions Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State

Samacheer Kalvi 11th Chemistry Gaseous State Textual Evaluation Solved

I. Choose the correct answer from the following:

Question 1.
Gases deviate from ideal behavior at high pressure. Which of the following statement (s) is correct for non – ideality?
(a) at high pressure the collision between the gas molecule become enormous
(b) at high pressure the gas molecules move only in one direction
(c) at high pressure, the volume of gas become insignificant
(d) at high pressure the inter molecular interactions become significant
Answer:
(d) at high pressure the inter molecular interactions become significant

Question 2.
Rate of diffusion of a gas is …………
(a) directly proportional to its density
(b) directly proportional to its molecular weight
(c) directly proportional to its square root of its molecular weight
(d) inversely proportional to the square root of its molecular weight
Answer:
(d) inversely proportional to the square root of its molecular weight

Question 3.
Which of the following is the correct expression for the equation of state of van der Waals gas?
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State
Answer:
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State

Question 4.
When an ideal gas undergoes unrestrained expansion, no cooling occurs because the molecules ………….
(a) are above inversion temperature
(b) exert no attractive forces on each other
(c) do work equal to the loss in kinetic energy
(d) colide without loss of energy
Answer:
(b) exert no attractive forces on each other

Question 5.
Equal weights of methane and oxygen is mixed in an empty container at 298 K. The fraction of total pressure exerted by oxygen ………..
(a) 1/3
(b) 1/2
(c) 2/3
(d) 1/3 × 273 × 298
Answer:
(a) 1/3
Hint:
mass of methane = mass of oxygen = a
number of moles of methane = \(\frac {a}{16}\)
number of moles of Oxygen = \(\frac {a}{32}\)
mole fraction of Oxygen = Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State
Partial pressure of oxygen = mole fraction x Total Pressure = \(\frac {1}{3}\)P

For an ideal gas, the partial pressure formula relationship is called Henry’s Law.

Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State

Question 6.
The temperatures at which real gases obey the ideal gas laws over a wide range of pressure is called …………
(a) Critical temperature
(b) Boyle temperature
(c) Inversion temperature
(d) Reduced temperature
Answer:
(b) Boyle temperature
Hint:
The temperature at which real gases obey the ideal gas laws over a wide range of pressure is called Boyle temperature

Question 7.
In a closed room of 1000 m3 a perfume bottle is opened up. The room develops a smell. This is due to which property of gases?
(a) Viscosity
(b) Density
(c) Diffusion
(d) None
Answer:
(c) Diffusion

Question 8.
A bottle of ammonia and a bottle of HCl connected through a long tube are opened simultaneously at both ends. The white ammonium chloride ring first formed will be ………….
(a) At the center of the tube
(b) Near the hydrogen chloride bottle
(c) Near the ammonia bottle
(d) Throughout the length of the tube
Answer:
(b) Near the hydrogen chloride bottle
Hint:
Rate of diffusion α 1/√m
mNH3  = 17
mHCl = 36.5
γNH3  > γHCl
Hence white fumes first formed near hydrogen chloride.

Question 9.
The value of universal gas constant depends upon ………..
(a) Temperature of the gas
(b) Volume of the gas
(c) Number of moles of the gas
(d) units of Pressure and volume
Answer:
(d) units of Pressure and volume

Question 10.
The value of the gas constant R is …………
(a) 0.082 dm3 atm.
(b) 0.987 cal mol-1 K-1
(c) 8.3 J mol-1K-1
(d) 8 erg mol-1K-1
Answer:
(c) 8.3 J mol-1K-1

Question 11.
Use of hot air balloon in sports at meteorological observation is an application of
(a) Boyle’s law
(b) Newton’s law
(c) Kelvin’s law
(d) Brown’s law
Answer:
(a) Boyle’s law

Question 12.
The table indicates the value of van der Waals constant ‘a’ in (dm3)2 atm. mol-2
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State
The gas which can be most easily liquefied is ………….
(a) O2
(b) N2
(c) NH3
(d) CH4
Answer:
(c) NH3
Hint:
Higher the value of ‘a’, greater the intermolecular force of attraction, easier the liquefaction. Option (c) is correct

Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State

Question 13.
Consider the following statements.
(i) Atmospheric pressure is less at the top of a mountain than at sea level
(ii) Gases are much more compressible than solids or liquids
(iii) When the atmospheric pressure increases the height of the mercury column rises Select the correct statement.
(a) (i) and (ii)
(b) (ii) and (iii)
(c) (i) and (iii)
(d) (i), (ii) and (iii)
Answer:
(d) (i), (ii) and (iii)

Question 14.
Compressibility factor for CO2 at 400 K and 71.0 bar is 0.8697. The molar volume of CO2 under these conditions is ………..
(a) 22.04 dm3
(b) 2.24 dm3
(c) 0.41 dm3
(d) 19.5 dm3
Answer:
(c) 0.41 dm3
Compressibility factor (z) = \(\frac {Pv}{nRT}\)
V = \(\frac {z x nRT }{p}\)
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State
V = 0.41 dm3

Question 15.
If temperature and volume of an ideal gas is increased to twice its values, the initial pressure P becomes ………….
(a) 4P
(b) 2P
(c) P
(d) 3P
Answer:
(c) P
Hint:
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State
P2 = P2 Option (c)

Question 16.
At identical temperature and pressure, the rate of diffusion of hydrogen gas is 3\(\sqrt{3}\) times that of a hydrocarbon having molecular formula What is the value of n?
(a) 8
(b) 4
(c) 3
(d) 1
Answer:
(b) 4.
Hint:
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State
Squaring on both sides and rearranging
27 x 2 = mCnH2n-2
54 = n(12) + (2n-2)(l)
54 = 12n+2n – 2
54 = 14n – 2
n = (54 + 2)/14 = 56/14 = 4

Question 17.
Equal moles of hydrogen and oxygen gases are placed in a container, with a pin-hole through which both can escape what fraction of oxygen escapes in the time required for one-half of the hydrogen to escape. (NEET phase 1)
(a) 3/8
(b) 1/2
(c) 1/8
(d) 1/4
Answer:
(c) 1/8
Hint:
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State
The fraction of oxygen that escapes in the time required for one half of the hydrogen to escape is 1/8

Question 18
The variation of volume V, with temperature T, keeping pressure constant is called the coefficient of thermal expansion ie α = \(\frac{1}{V}\left(\frac{\partial V}{\partial T}\right)_{P}\)For an ideal gas α is equal to ………..
(a) T
(b) 1/T
(c) P
(d) none of these
Answer:
(b) 1/T
Hint:
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State-

Question 19.
Four gases P, Q, R and S have almost same values of ‘b’ but their ‘a’ values (a, b are Van der Waals Constants) are in the order Q < R < S < P. At a particular temperature, among the four gases the most easily liquefiable one is ………….
(a) P
(b) Q
(c) R
(d) S
Answer:
(a) P
Hint:
Greater the ‘a’ value, casier the liquefaction

Question 20.
Maximum deviation from ideal gas is expected from (NEET)
(a) CH4(g)
(b) NH3(g)
(c) H2(g)
(d) N2(g)
Answer:
(b) NH3(g)

Question 21.
The units of Van der Waals constants ‘b’ and ‘a’ respectively
(a) mol L-1 and L atm2 mol-1
(b) mol L and L atm mol2
(c) mol-1 L and L2 atm mol-1
(d) none of these
Answer:
(c) mol-1 L and L2 atm mol-1
Hint:
an2/V2 atm
a = atm L2/mol2 = L2 mol-2 atm
nb = L
b = L /mol = L mol-1

Question 22.
Assertion : Critical temperature of CO2 is 304 K, it can be liquefied above 304 K.
Reason : For a given mass of gas, volume is to directly proportional to pressure at constant temperature.
(a) both assertion and reason arc true and reason is the correct explanation of assertion
(b) both assertion and reason are true but reason is not the correct explanation of assertion
(c) assertion is true but reason is false
(d) both assertion and reason are false
Answer:
(d) both assertion and reason are false
Hint:
Correct Statement: Critical temperature of CO2 is 304 K. It means that CO2 cannot be liquefied above 304 K, whatever the pressure may applied. Pressure is inversely proportional to volume.

Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State

Question 23.
What is the density of N, gas at 227°C and 5.00 atm pressure? (R = 0.082 L atm K-1 mol-1)
(a) 1.40 g/L
(b) 2.81 g/L
(c) 3.41 g/L
(d) 0.29 g/L
Answer:
(c) 3.41 g/L
Hint:
Density = \(\frac {Mass}{Volume}\)
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State

Question 24.
Which of the following diagrams correctly describes the behaviour of a fixed mass of an ideal gas ? (T is measured in K)
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State
Answer:
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State
For a fixed mass of an ideal gas V α T
P α 1/V
and PV = Constant

Question 25.
25 g of each of the following gases are taken at 27°C and 600 mm Hg pressure. Which of these will have the least volume?
(a) HBr
(b) HCl
(c) HF
(d) HI
Answer:
(d) HI
Hint:
At a given temperature and pressure
Volume α number of moles
Volume α Mass / Molar mass
Volume α 28 / Molar mass
i.e. if molar mass is more , volume is less. Hence Hl has the least volume.

II. Answer these questions briefly.

Question 26.
State Boyle’s law.
Answer:
At a given temperature the volume occupied by a fixed mass of a gas is inversely proportional to its pressure.
Mathematically, Boyle’s law can be written as
V ∝ \(\frac{1}{P}\)     …………..(1)
(T and n are fixed, T-temperature, n-number of moles)
V = k × \(\frac{1}{P}\) …………(2)
k – proportionality constant
PV = k (at constant temperature and mass)

Question 27.
A balloon filled with air at room temperature and cooled to a much lower temperalure can be used as a model for Charles’ law.
Answer:
Charles’ law:

  • V T at constant P and n (or) \(\frac {V}{T}\) = Constant
  • A balloon filled with air at room temperature and cooled to a much lower temperature. the size of the balloon is reduced. Because if the temperature of the gas decreases, the volume also decreases in a direct proportion.
  • When temperature is reduced, the gas molecules inside in over slower due to decreased temperature and hence the volume decreases.

Question 28.
Name two items that can serve as a model for Gay Lussac’s law and explain.
Answer:
Gay Lussac’s law:
1. P α T at constant volume (or) = \(\frac {V}{T}\)
2. Example – 1:
You fill the car type completely full of air on the hottest day of summer. The type cannot change it shape and volume. But when winter comes, the pressure inside the lyre is reduced and the shape is also reduced. This confirms that pressure and temperature are direct related to each other.
3. Example – 2:
The egg in the bottle experiment.
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State
A glass bottle is taken, inside the bottle put some pieces of cotton with fire. Then place a boiled egg (shell removed) at the top of the bottle. The temperature inside the bottle increases from the fire, rising (he pressure. By scaling the bottle with egg, the fire goes on, dropping the temperature and pressure. This causes the egg to be sucked into the bottle.
P α T is proved (or) = \(\frac{P_{1}}{V_{1}}=\frac{P_{2}}{V_{2}}\)

Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State

Question 29.
Give the mathematical expression that relates gas volume and moles. Describe in words what the mathematical expression means.
Answer:
The mathematical expression that relates gas volume and moles is Avogadro’s hypothesis. It may be expressed as
V ∝ n,
\(\frac{V_{1}}{n_{1}}=\frac{V_{2}}{n_{2}}\) = constant
where V1 and n1 are the volume and number of moles of a gas and V2 and n2 are a different set of values of volume and number of moles of the same gas at the same temperature and pressure.

Question 30.
What are ideal gases? In what way real gases differ from ideal gases.
Answer:

  1. Ideal gases are the gases that obey gas laws or gas equation PV = nRT.
  2. Real gases do not obey gas equation. PV = nRT.
  3. The deviation of real gases from ideal behaviour is measure in terms of a ratio of PV to nRT. This is termed as compression factor (Z). Z = \(\frac {PV}{nRT}\)
  4. For ideal gases Z = 1.
  5. For real gases Z > 1 or Z < 1. For example, at high pressure real gases have Z >1 and at intermediate pressure Z < 1.
  6.  Above the Boyle point Z> 1 for real gases and below the Boyle point, the real gases first show a decrease for Z, reaches a minimum and then increases with the increase in pressure.
  7. So, it is clear that at low pressure and high temperature, the real gases behave as ideal gases.

Question 31.
Can a Van der Waals gas with a = 0 be liquefied? Explain.
Answer:
If the van der Waals constant (a) = 0 for gas, then it behaves ideally, (i.e.,) there is no intermolecular forces of attraction. So it cannot be liquefied. Moreover,
Pc = \(\frac{a}{27 b^{2}}\)
If a = 0, then Pc = 0; therefore it cannot he liquefied.

Question 32.
Suppose there ¡s a tiny sticky area on the wan of a container of gas. Molecules hitting this area stick there permanently. Is the pressure greater or less than on the ordinary area of walls?
Answer:

  • Molecules hitting the tiny sticky area on the wall of the container of gas moves faster as they get closer to adhesive surface, but this effect is not permanent.
  • The pressure on the sticky wall is greater than on the ordinary area of walls.

Question 33.
Explain the following observations?
(a) Aerated water bottles are kept under water during summer
(b) Liquid ammonia bottle is cooled before opening the seal
(c) The type of an automobile is inflated to slightly lesser pressure in summer than in winter
(d) The size of a weather balloon becomes larger and larger as it ascends up into larger altitude
Answer:
(a) Aerated water bottles contains excess dissolved oxygen and minerals which dissolved under certain pressure and if this pressure suddenly decrease due to change in atmospheric pressure, the bottle will certainly burst with decrease the amount of dissolved oxygen in water, this tends to change the aerated water into normal water.

(b) The vapour pressure of ammonia at room temperature is very high and hence the ammonia will evaporate unless the vapour pressure is decreased. On cooling the vapour pressure decreases so that the liquid remains in the same state. Hence, the bottle is cooled ’ before opening.

(c) In Summer due to hot weather conditions, the air inside the tyre expands to large volumes due to heat as compared to winter, therefore, inflated to lesser pressure in summer.

(d) As we move to higher altitude, the atmospheric pressure decreases, therefore the balloon can J easily expand to large volume.

Question 34.
Give suitable explanation for the following facts about gases.
(a) Gases don’t settle at the bottom of a container
(b) Gases diffuse through all the space available to them and
(c) Explain with an increase in temperature
Answer:
(a) Gases by definition are the least dense state of matter. They have negligible intermolecular forces of attraction. So they are all free to roam separately. So the least dense gas particles will not sink at the bottom of a container.

(b) When a sample of a gas introduced to one part of a closed container, its molecules very quickly disperse throughout the container, this process by which molecules disperse in space in response to differences in concentration is called diffusion. For e.g., you can smell perfume in a room, because it difluses into the air totally inside the room.

(c) Diffusion is faster at higher temperature because the gas molecules have greater kinetic energy. Since heat increase the motion, then diffusion happens faster.

Question 35.
Suggest why there ¡s no hydrogen (H2) in our atmosphere. Why does the moon have no atmosphere?
Answer:
Hydrogen has a tendency to combine with oxygen from water vapour. Hence, the presence of hydrogen is negligible in the atmosphere. The gravitational pull in the moon is very less and hence, there is no atmosphere in the moon.

Question 36.
Explain whether a gas approaches ideal behaviour or deviates from ideal behaviour if –
(a) it is compressed to a smaller volume at constant temperature
(b) the temperature is raised while keeping the volume constant
(c) more gas is introduced into the same volume and at the same temperature
Answer:
(a) it a gas is compressed to a smaller volume at constant temperature, pressure is increased. At high pressure with a smaller volume, the gas deviates from ideal behaviour.

(b) If a gas temperature is raised keeping the volume constant, the pressure of the gas will increase. At high pressure, the gas deviates from ideal behaviour.

(c) if more gas is introduced into the same volume and at the same temperature, the number of moles are increasing. if the volume remains same, the increased number of moles collide with each other and kinetic energy increases and pressure decreases. At increased pressure, the gas deviates from ideal behaviour.

Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State

Question 37.
Which of the following gases would you expect to deviate from ¡deal behaviour under conditions of low-temperature FCl2, or Br2? Explain.
Answer:
Bromine has a greater tendency to deviate from ideal behavior at low temperatures. The compressibility factor tends to deviate from unity for bromine.

Question 38.
Distinguish between diffusion and effusion.
Answer:
Diffusion:

  • Diffusion is the spreading of molecules of a substance throughout a space or a second substance.
  • Diffusion refers to the ability of the gases to mix with each other.
  • E.g.. Spreading of something such as brown tea liquid spreading through the water in a tea cup.

Effusion:

  • Effusion is the escape of gas molecules through a very small hole in a membrane into an evacuated area.
  • Effusion is a ability of a gas to travel through a small pin-hole.
  • E.g., pouring out something like the soap studs bubbling out from a bucket of water.

Question 39.
Aerosol cans carry clear warning of heating of the can. Why?
Answer:
Aerosol cans carry clear warning of heating of the can. As the temperature rises, pressure in the can will increase and ambient temperatures about 120°F may lead to explosions. So aerosol cans should always be stored in dry areas where they will not be exposed to excessive temperatures. You should never throw an aerosol can onto a fire or leave it in the direct sunlight. even it is empty. This is because the pressure will build up so much that the can will burst. It is due to 2 reasons.

  • The gas pressure increases.
  • More of the liquefied propellant turns into a gas.

Question 40.
When the driver of an automobile applies brake, the passengers are pushed toward the front of the car but a helium balloon is pushed toward back of the car. Upon forward acceleration the passengers are pushed toward the front of the car. Why?
Answer:
Helium floats because it is buoyant; its molecules are lighter than the nitrogen and oxygen molecules of our atmosphere and so they rise above it. In the car, it’s the air molecules that are actually getting pulled and pushed around by gravity as the result of the accelerating frame.

That means it moves in a direction opposite to the force on the surrounding air. Normally, the air is pulled downwards due to gravity, which pushes the balloon upwards. In this case, the surrounding air in the car is pulled forward by the deceleration of the car, which pushes the helium balloon backward.

Question 41.
Would it be easier to drink water with a straw on the top of Mount Everest?
Answer:
It is difficult to drink water with a straw on the top of Mount Everest. This is because the reduced atmospheric pressure is less effective in pushing water into the straw at the top of the mountain because gravity falls off gradually with height. The air pressure falls off, there isn’t enough atmospheric pressure to push the water up in the straw all the way to the mouth.

Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State

Question 42.
Write the Van der Waals equation for a real gas. Explain the correction term for pressure and volume.
Answer:
Van der Waals equation of state for real gases is
\(\left(P+\frac{a n^{2}}{V^{2}}\right)(V-n b)\) = nRT

Correction term for pressure:
\(\frac{\mathrm{an}^{2}}{\mathrm{V}^{2}}\) is the pressure correction. It represents the intermolecular interaction that causes the non ideal behaviour.

Correction term for Volume:
V – nb is the volume correction. it is the effective volume occupied by real gas.

Question 43.
Derive the values of critical constants from the Van der Waals constants.
Answer:
Derivation of critical constants from the Van der Waals constants:
Van der Waals equation is,
\(\left(P+\frac{a n^{2}}{V^{2}}\right)(V-n b)\) = nRT for 1 mole
From this equation, the values of critical constant PCVC and TC arc derived in terms of a and b the Van der Waals constants.
\(\left(P+\frac{a n^{2}}{V^{2}}\right)(V – b)\) = RT ………..(1)
On expanding the equestion (1)
P V + \(\frac {a}{V}\) – pb – \(\frac{\mathrm{ab}}{\mathrm{V}^{2}}\) – RT = 0 ………(2)
Multiplying eqestion (2) by \(\frac{V^{2}}{P}\),
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State
equation (3) is rearranged in the powers of V
V3 – \(\left[\frac{\mathrm{RT}}{\mathrm{P}}+\mathrm{b}\right]\) V2 + \(\frac {aV}{P}\) –
= 0 ………..(4)
The above equation (4) is an cubic equation of V, which can have three roots. At the critical point. all the three values of V are equal to the critical volume VC.
i.e. V = VC.
V – VC = O ……….(5)
(V – VC)3 = O ………(6)
(V3 – 3VCV2 + 3VC3V – VC3 = 0 ………(7)
As the equation (4) is identical with equation (7), comparing the ‘V’ ternis in (4) and (7),
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State
Divide equation (11) by (10)
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State
When equation (12) is substituted in (10)
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State
substituting the values of Vc and Pc in equation (9)
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State
Critical constant a and b can be calculated using Van der Waals Constant as follows:
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State

Question 44.
Why do astronauts have to wear protective suits when they are on the surface of moon?
Answer:
Astronauts must wear spacesuits whenever they leave a spacecraft and are exposed to the environment of the moon. On the moon, there is no air to breathe and no air pressure. Moon is extremely cold and filled with dangerous radiation. Without protection, an astronaut would quickly die in space. Spacesuits are specially designed to protect astronauts from the cold, radiation, and low pressure in space. They also provide air to breathe. Wearing a spacesuit allows an astronaut to survive and work on the moon.

Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State

Question 45.
When ammonia combines with HCl, NH4 Cl is formed as white dense fumes. Why do more funies appear near HCl?
Answer:

  1. When ammonia combines with HCl, NH4 Cl is formed as white dense fumes. The reaction takes place in neutralization between a weak base and a strong acid.
  2. The property of the gas is diffusion.
  3. Diffusion of gases Ammonia and hydrogen chloride. Concentrated ammonia solution is placed on a pad in one end of a tube and concentrated HCl on the pad at the other.
  4. After about a minute, the gases diffuses far enough to meet and a ring of solid ammonium chloride is formed near the HCl end.

Question 46.
A sample of gas at 15°C at 1 atm has a volume of 2.58 dm3. Vhen the temperature is raised to 38°C at I atm does the volume of the gas increase? if so, calculate the final volume.
Answer:
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State
V2 = 2.78 dm3 i.e. volume increased from 2.58 dm3 to 2.78 dm3.

Question 47.
A sample of gas has a volume of 8.5 dm3 at an unknown temperature. When the sample is submerged in ice water at 0°C, its volume gets reduced to 6.37 dm3. What ¡s its initial temperature?
Answer:
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State
T1 = 364.28 K

Question 48.
Of two samples of nitrogen gas, sample A contains 1.5 moles of nitrogen in a vessel of volume of 37.6 dm3 at 298K, and the sample B is in a vessel of volume 16.5 dm3 at 298 K. Calculate the number of moles in sample B.
Answer:
nA = 1.5 mol nB = ?
VA = 37.6 dm3 VB = 16.5 dm3
(T = 298 K constant)
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State

Question 49.
Sulphur hexafluoride is a colourless, odourless gas; calculate the pressure exerted by 1.82 moles of the gas in a steel vessel of volume 5.43 dm3 at 69.5°C, assuming ¡deal gas behaviour.
Answer:
n = 1.82 mole
V = 5.43 dm3
T = 69.5 + 273 = 342.5
P = ?
PV = nRT
P = \(\frac {nRT}{V}\)
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State
P = 94.25 atm.

Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State

Question 50.
Argon is an inert gas used in light bulbs to retard the vapourlzation of the tungsten filament. A certain light bulb containing argon at 1.2 atm and 18°C is heated to 85°C at constant volume. Calculate its final pressure in atm.
Answer:
P1 = 1.2 atm
T1 = 18°C + 273 = 291 K
T2 = 85°C + 273 = 358 K
P2 = ?
\(\frac{P_{1}}{T_{1}}=\frac{P_{2}}{T_{2}}\)
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State-

Question 51.
A small bubble rises from the bottom of a lake, where the temperature and pressure are 6°C and 4 atm. to the water surface, where the temperature is 25°C and pressure is 1 atm. Calculate the final volume in (mL) of the bubble, if its initial volume is 1.5 mL.
Answer:
T1 = 6°C + 273 = 279 K
P1 = 4 atm V1 = 1.5m
T2 = 25°C + 273 = 298 K
P2 = 1 atm V 1 = ?
\(\frac{P_{1} V_{1}}{T_{1}}=\frac{P_{2} V_{2}}{T_{2}}\)
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State-
V2 = 6.41 mol.

Question 52.
Hydrochloric acid is treated with a metal to produce hydrogen gas. Suppose a student carries out this reaction and collects a volume of 154.4 x 10-3 dm3 of a gas at a pressure of 742 mm of Hg at a temperature of 298 K. What mass of hydrogen gas (in mg) did the student collect?
Answer:
V = 154.4 x 10-3dm3
P = 742 mm of Hg
T = 298 K m = ?
n = \(\frac{PV}{RT}\) = Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State-
= 0.006 mol
n = \(\frac{PV}{RT}\)
n = \(\frac{Mass}{Molar Mass}\)
Mass = n x Molar mass
= 0.006 x 2.016
= 0.0121 g = 12.1 mg.

Question 53.
It takes 192 sec for an unknown gas to diffuse through a porous wall and 84 sec for N2 gas to effuse at the same temperature and pressure. What is the molar mass of the unknown gas?
Answer:
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State

Question 54.
A tank contains a mixture of 52.5 g of oxygen and 65.1 g of CO2 at 300 K the total pressure in the tank ¡s 9.21 atm. Calculate the partial pressure (in atm.) of each gas in the mixture.
Answer:
mO2 = 52.5 g
PO2 = ?
mCO2 = 65.1 g
PCO2 = ?
T = 300 K P = 9.21 atm
PO2 = XO2 x total pressure
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State-
PO2 = XO2 x Total pressure
= 0.53 x 9.21 atm = 4.88 atm
PCO2 = XCO2 x Total pressure
= 0.47 x 9.21 atm = 4.33 atm

Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State

Question 55.
A combustible gas Is stored in a metal tank at a pressure of 2.98 atm at 25 °C. The tank can withstand a maximum pressure of 12 atm after which it will explode. The building in which the tank has been stored catches fire. Now predict whether the tank will blow up first or start melting? (Melting point of the metal = 1100 K).
Answer:
T1 = 298 K;
P1 = 2.98 atm;
T2 = 1100K;
P2 = ?
\(\frac{P_{1}}{T_{1}}=\frac{P_{2}}{T_{2}}\)
P2 = \(\frac{P_{1}}{T_{1}} \times T_{2}\)
= \(\frac{2.98 \mathrm{atm}}{298 \mathrm{K}} \times 1100 \mathrm{K}\) = 11 atm
At 1100 K, the pressure of the gas inside the tank will become 11 atm. Given that tank can withstand a maximum pressure of 12 atm, the tank will start melting first.

In Text Questions – Evaluate Yourself

Question 1.
Freon-I 2, the compound widely used in the refrigerator system as coolant causes depletion of ozone layer. Now It has been replaced by eco-friendly compounds. Consider 1.5 dm3 sample of gaseous freon at a pressure of 0.3 atm. If the pressure is changed to 1.2 atm. at a constant temperature, what will be the volume of the gas increased or decreased?
Answer:
Volume of freon (V1) = 1.5 dm3
Pressure (P1) = 0.3 atm
‘T’ is constant
P2 = 1.2 atm
V2 = ?
P1V1 = P2V2
V2 = \(\frac{P_{1} V_{1}}{P_{2}}\)
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State-
= 0.375 dm3
Volume decreased from 1.5 dm3 to 0.375 dm3

Question 2.
Inside a certain automobile engine, the volume of air in a cylinder is 0.375 dm3, when the pressure is 1.05 atm. When the gas is compressed to a volume of 0.125 dm3 at the same temperature, what is the pressure of the compressed air?
Answer:
V1 = 0.375dm3
V2 = 0.125 dm3
P1 = 1.05 atm
P2 = ?
T – Constant
P1V1 = P2V2
P2 = \(\frac{P_{1} V_{1}}{V_{2}}=\frac{10.5 \times 0.375}{0.125}\)
= 3.15 atm.

Question 3.
A sample of gas has a volume of 3.8 dm3 at an unknown temperature. When the sample is submerged in ice water at 0°C, its volume gets reduced to 2.27 dm3. What is its initial temperature?
Answer:
V1 = 3.8 dm3
T2 = 0°C = 273K
T1 = ? V2 = 2.27dm3
\(\frac{V_{1}}{T_{1}}=\frac{V_{2}}{T_{2}}\)
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State-
T1 = 457 K

Question 4.
An athlete in a kinesiology research study has his lung volume of 7.05 dm3 during a deep inhalation. At this volume the lungs contain 0.312 mole of air. During exhalation the volume of his Jung decreases to 2.35 dm3 How many moles of air does the athlete exhale during exhalation? (assume pressure and temperature remain constant)
Answer:
V1 = 7.05 dm3
V2 = 2.35 dm3
n1 = 0.312 mol
n1 =?
‘P’ and ‘T’ are constant
\(\frac{V_{1}}{n_{1}}=\frac{V_{2}}{n_{2}}\)
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State-
n2 = 0.104 mol
Number of moles exhaled = 0.312 – 0.104 = 0.208 moles

Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State

Question 5.
A small bubble rises from the bottom of a lake, where the temperature and pressure are 8° C and 6.4 atm. to the water surface, where the temperature ¡s 25°C and pressure is 1 atm. Calculate the final volume in (ml) of the bubble, if its initial volume is 2.1 ml.
Answer:
T1 = 8°C = 8 + 273 = 281K
P1 = 6.4atm V1 = 2.1 mol
T2 = 25°C = 25 + 273 = 298 K
P2 = 1 atm
V2 = ?
\(\frac{P_{1} V_{1}}{T_{1}}=\frac{P_{2} V_{2}}{T_{2}}\)
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State-
V2 = 14.25 ml

Question 6.
(a) A mixture of He and O2 were used ¡n the ‘air’ tanks of underwater divers for deep dives. For a particular dive 12 dm3 of O2 at 298 K, I atm. and 46 dm3 of He, at 298 K, 1 aim. were both pumped into a 5 dm3 tank. Calculate the partial pressure of each gas and the total pressure In the tank at 298 K
Answer:
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State
P = 1 atm
Vtotal = 5 dm3
PO2 = XO2 x Ptotal
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State
PHe = 3.54 atm

Question 6.
(b) A sample of solid KClO3 (potassium chlorate) was heated in a test tube to obtain O2 according to the reaction 2KClO3 → 2KCl(s) + 3O2 The oxygen gas was collected by downward displacement of water at 295 K. The total pressure of the mixture is 772 mm of Hg. The vapour pressure of water is 26.7 mn of Hg at 300K. What is the partial pressure of the oxygen gas?
Answer:
2KCl3(s) → 2KCl(s) 3O3(g)
Ptotal = 772 mm Hg
PH2O = 26.7 mm Hg
Ptotal = PO2 + PH2O
PO2 = Ptotal – PH2O
P1 = 26.7 mm Hg
T1 = 300 K
T2 = 295 K
P2 = ?
\(\frac{P_{1}}{T_{1}}=\frac{P_{2}}{T_{2}}\)
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State
P2 = 26.26 mm Hg
∴ PO2 = 772 – 26.26
= 745.74 mm Hg

Question 7.
A flammable hydrocarbon gas of particular volume is found to diffuse through a small hole in 1.5 minutes. Under the same conditions of temperature and pressure an equal volume of bromine vapour takes 4.73 min to diffuse through the same hole. Calculate the molar mass of the unknown gas and suggest what this gas might be, (Given that molar mass of bromine = 159.8 g/ mole)
Answer:
t1 = 1.5 minutes (gas)hydrocarbon
t2 = 4.73 minutes (gas)Bromi
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State
n (12) + (2n + 2) 1 = 16 (general formula for hydrocarbon CnH2n+2)
12n + 2n + 2 = 16
14n = 16 – 2
14n = 14
n = 1
The hydrocarbon is C1H2(1) + 2 = CH4

Question 8.
Critical temperature of H2O, NH3 and CO2 are 647.4, 405.5 and 304.2 K, respectively. When we start cooling from a temperature of 700 K which will liquefy first and which will liquefy finally?
Answer:
Critical temperature of a gas is defined as the temperature above which it cannot be liquefied even at high pressures.
∴ When cooling starts from 700 K, H2O vill liquefied first, then followed by ammonia and finally carbon dioxide will liquefied.

Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State

In-Text Example Problems

Question 9.
In the below figure, let us find the missing parameters [volume in (b) and pressure in (c)]
P1 = 1 atm P2 = 2 atm P3 = ? atm
V1 I dm3  V2 =? dm3 V3 = 0.25 dm3
T1 = 298 K T2 = 298 K T3 = 298 K
Solution:
According to Boyle’s law, at constant temperature for a given mass of gas at constant temperature,Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State
P1V1 = P2V2 = P3V3
I atm x 1 dm3 = 2 atm x V2 = P3x 0.25 dm3
∴ 2 atm x V2 = 1 atm x 1 dm3
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State
V2 = 0.5 dm3
and P3 x 0.25 dm3 = 1 atm x 1 dm3
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State
P3 = 4atm

Question 10.
In the below figure, let us find the missing parameters [volume in (b) and temperature in (c)]
P1 = 1 atm P2 = 1 atm P3 = 1 atm
V1 = 0.3dm3 V2 = ?dm3 V3 = 0.15dm3
T1 = 200K T2 = 300 K T3 = ? K
Answer:
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State
According to Charles law,
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State
T3 = 100k

Question 11.
Calculate the pressure exerted by 2 moles of sulphur hexafluoride in a steel vessel of volume 6 dm3 at 70°C assuming It is an ideal gas.
Answer:
We will use the ideal gas equation for this calculation as below:
P = \(\frac {nRT}{V}\)
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State
= 9.39 atm.

Question 12.
A mixture of gases contains 4.76 mole of Ne, 0.74 mole of Ar and 2.5 mole of Xe. Calculate the partial pressure of gases, if the total pressure is 2 atm. at a fixed temperature. Solve this problem using Dalton’s law.
Answer:
PNe = XNe PTotal
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State
PNe = XNe PTotal = 0.595 x 2 = 1.19 atm.
PNe = XNe PTotal = 0.093 x 2 = 0. 186 atm.
PNe = XNe PTotal = 0.312 x 2 = 0.624 atm.

Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State

Question 13.
An unknown gas diffuses at a rate of 0.5 time that of nitrogen at the same temperature and pressure. Calculate the molar mass of the unknown gas.
Answer:
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State

Question 14.
If a scuba diver takes a breath at the surface filling his lungs with 5.82 dm3 of air what volume will the air in his lungs occupy when he drives to a depth, where the pressure ¡s 1.92 atm. (assume temperature is constant and the pressure at the surface is exactly 1 atm.)
Solution :
Temperature = Constant
Pressure at the surface = 1 atm – P1
Pressure at the depth = 1.92 atm – P2
Vdlume of air breathing at the surface of the air = 5.82 dm3 – V1
Volume of air breathing at the depth = V2 = ?
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State
V1 = 3.03 dm3
The volume of air scuba diver’s lung occupy = 3.03 dm3

Question 15.
Inside a certain automobile engine, the volume of air in a cylinder is 0.475 dm3, when the pressure is 1.05 atm. When the gas is compressed, the pressure increased to 5.65 atm. at the same temperature. What is the volume of compressed air?
Solution:
Volume of air in the cylinder 0.475 dm3 – V1
Pressure of air P1 = 1.05 atm
Increased pressure P2 = 5.65 atm
Volume of air compressed V2 = ?
P1V1 = P2V2
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State
V2 = 0.08827 dm3
Compressed volume of air = 0.08 827 dm3

Samacheer Kalvi 11th Chemistry Gaseous State Additional Questions Solved

I. Choose the correct answer.

Question 1.
The approximate volume percentages of nitrogen and oxygen in the atmosphere of air are _______ and ______ respectively.
(a) 21, 68
(b) 21, 78
(c) 78, 2
(d) 80, 21
Answer:
(c) 78, 2

Question 2.
The average kinetic energy of the gas molecule is …………
(a) inversely proportional to its absolute temperature
(b) directly proportional to its absolute temperature
(c) equal to the square of its absolute temperature
(d) All of the above
Answer:
(b) directly proportional to Its absolute temperature

Question 3.
The compound widely used in the refrigerator as coolant is
(a) Freon-2
(b) Freon-12
(c) Freon-13
(d) Freon-14
Answer:
(b) Freon-12

Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State

Question 4.
At constant temperature, the pressure of the gas is reduced to one-third, the volume
(a) reduce to one-third
(b) increases by three times
(c) remaining the same
(d) cannot be predicted
Answer:
(b) increases by three times

Question 5.
Hydrogen is placed in the ______ of the periodic table.
(a) Group -1
(b) group-17
(c) group-18
(d) group-2
Answer:
(a) Group -1

Question 6.
Viscosity of a liquid is a measure of ……………
(a) repulsive forces between the liquid molecules
(b) frictional resistance
(c) intermolecular forces between the molecules
(d) none of the above
Answer:
(b) frictional resistance

Question 7.
At constant temperature for a given mass, for each degree rise in temperature, all gases expand by of their volume at 0°C.
(a) 273
(b) 298
(c) \(\frac{1}{273}\)
(d) \(\frac{1}{298}\)
Answer:
(c) \(\frac{1}{273}\)

Question 8.
In Vander Waals equation of state for a non-ideal gas the net force of attraction among the molecules is given by ………..
(a) \(\frac{\mathrm{an}^{2}}{\mathrm{V}^{2}}\)
(b) P + \(\frac{\mathrm{an}^{2}}{\mathrm{V}^{2}}\)
(c) P – \(\frac{\mathrm{an}^{2}}{\mathrm{V}^{2}}\)
(d) – \(\frac{\mathrm{an}^{2}}{\mathrm{V}^{2}}\)
Answer:
(a) \(\frac{\mathrm{an}^{2}}{\mathrm{V}^{2}}\)

Question 9.
‘At constant volume, the pressure of a fixed mass of a gas is directly proportional to temperature”. This statement is
(a) Charle’s law
(b) Boyle’s law
(c) Gay-Lussac’s law
(d) Dalton’s law
Answer:
(c) Gay-Lussac’s law

Question 10.
Which of the following gases will have the lowest rate of diffusion?
(a) H2
(b) N2
(c) F2
(d) O2
Answer:
(c) F2

Question 11.
A mixture of gases containing 4 moles of hydrogen and 6 moles of oxygen. The partial pressure of hydrogen, if the total pressure is 5 atm, is
(a) 10 atm
(b) 0.4 atm
(c) 20 atm
(d) 2 atm
Answer:
(d) 2 atm

Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State

Question 12.
Which of the following is a diatomic gas in nature?
(a) Oxygen
(b) Ozone
(c) Helium
(d) Radon
Answer:
(a) Oxygen

Question 13.
The property of a gas which involves the movement of the gas molecules through another gas is called
(a) effusion
(b) dissolution
(c) diffusion
(d) expansion
Answer:
(c) diffusion

Question 14.
Among the following groups which contains monoatomic gases?
(a) Group 17
(b) Group 18
(c) Group 1
(d) Group 15
Answer:
(b) Group 18

Question 15.
The rate of diffusion of a gas is inversely proportional to the
(a) square of molar mass
(b) square root of density
(c) square root of molar mass
(d) square of density
Answer:
(c) square root of molar mass

Question 16.
Which of the following gas is essential for our survival?
(a) N2
(b) H2
(c) O2
(d) He
Answer:
(c) O2

Question 17.
The deviation of real gases from ideal behavior is measured in terms of
(a) expansivity factor
(b) molar mass
(c) pressure
(d) compressibility factor
Answer:
(d) compressibility factor

Question 18.
Which of the following is not chemically inert?
(a) Helium
(b) Oxygen
(c) Argon
(d) Krypton
Answer:
(b) Oxygen

Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State

Question 19.
Match the List-I and List-II using the correct code given below the list.
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State

Answer:
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State

Question 20.
Ideal gas equation for ‘n’ moles is
(a) \(\frac{P}{R}=\frac{n T}{V}\)

(b) PV = \(\frac{n R}{T}\)

(c) \(\frac{V}{T}=\frac{n P}{R}\)

(d) \(\frac{P}{T}=\frac{n R}{V}\)
Answer:
(d) \(\frac{P}{T}=\frac{n R}{V}\)

Question 21.
The SI unit of pressure is ………..
(a) Nm-2  Kg-1
(b) Pascal
(c) bar
(d) atmosphere
Answer:
(b) Pascal

Question 22.
The volume correction introduced by Van der Waals is, Videal =
(a) V – nb
(b) V + nb
(c) \(\frac{V}{n b}\)
(d) b – nV
Answer:
(b) V + nb

Question 23.
The instrument used for measuring the atmospheric pressure is …………….
(a) lactometer
(b) barometer
(c) electrometer
(d) ammeter
Answer:
(b) barometer

Question 24.
The unit of Van der Waals constant V is
(a) atm lit mol-1
(b) atm lit2 mol-2
(c) atm lit-2 mol2
(d) atm lit-1 mol2
Answer:
(b) atm lit2 mol-2

Question 25.
Mathematical expression of Boyle’s law is ………….
(a) P1V1 = P2V2
(b) \(\frac {P}{V}\) = Constant
(c) \(\frac {V}{T}\) = Constant
(J) \(\frac {P}{T}\) = Constant
Answer:
(a) P1V1 = P2V2

Question 26.
Statement-I: If the volume of a fixed mass of a gas is reduced to half at constant temperature the gas pressure doubles.
Statement-II: If the volume is halved, the density of the gas is doubled.
(a) Statement-I and II are correct and Statement-II is the correct explanation of Statement-I
(b) Statement-I and II are correct but Statement-II is not the correct explanation of Statement-I
(c) Statement-I is correct but Statement-II is wrong
(d) Statement-I is wrong but Statement-II is correct
Answer:
(a) Statement-I and II are correct and Statement-II is the correct explanation of Statement-I

Question 27.
The gas used in the pressure-volume isotherm study of Andrew’s experiment is
(a) N2
(b) H2S
(c) NH3
(d) CO2
Answer:
(d) CO2

Question 28.
Which one of the following is absolute zero?
(a) 293 K
(b) 273 K
(c) – 273.15°C
(d) 0°C
Answer:
(c) – 273.15°C

Question 29.
The relationship between critical volume and Vander waals constant is
(a) Vc =\(\frac{a}{R b}\)
(b) Vc = 3b
(c) Vc = \(\frac{8 a}{27 R b}\)
(d) Vc = 8b
Answer:
(b) Vc = 3b

Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State

Question 30.
The ideal gas equation is …………..
(a) PV = RT for 1 mole
(b) P1 V1 = P2V2
(c) \(\frac {P}{T}\) = R
(d) P = P2 + P2 + P2
Answer:
(a) PV = RT for 1 mole

Question 31.
In the equation PV = nRT, which one cannot be numerically equal to R?
(a) 8.31 × 107 ergs K-1 mol-1
(b) 8.31 × 107 dynes cm K-1 mol-1
(c) 8.317J K-1 mol-1
(d) 8.317L atm K-1 mol-1
Answer:
(d) 8.317L atm K-1 mol-1

Question 32.
Mathematical expression of Graham’ s law is ……………….
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State
Answer:
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State

Question 33.
The number of moles of H2 in 0.224 L of hydrogen gas at STP (273 K, 1 atm) assuming ideal gas behavior is
(a) 1
(b) 0.1
(c) 0.01
(d) 0.001
Answer:
(c) 0.01

Question 34.
The value of compression factor Z is equal to ………….
(a) \(\frac {nRT}{PV}\)
(b) \(\frac {PV}{RT}\)
(c) PV x nRT
(d) \(\frac {PV}{nRT}\)
Answer:
(d) \(\frac {PV}{nRT}\)

Question 35.
To what temperature must a neon gas sample be heated to double its pressure, if the initial volume of gas at 75°C is decreased by 15.0% by cooling the gas?
(a) 319°C
(b) 592°C
(c) 128°C
(d) 60°C
Answer:
(a) 319°C

Question 36.
The value of critical temperature of carbon dioxide is …………
(a) 273 K
(b) 303.98 K
(c) 373 K
(d) – 80°C
Answer:
(b) 303.98 K

Question 37.
Match the List-I and List-II using the correct code given below the list.
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State
Answer:
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State

Question 38.
The rate of diffusion of gases A and B of molecular weight 36 and 64 are in the ratio
(a) 9 : 16
(b) 4 : 3
(c) 3 : 4
(d) 16 : 9
Answer:
(b) 4 : 3

Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State

Question 39.
The temperature below which a gas obey Joule Thomson effect is called …………..
(a) critical temperature
(b) standard temperature
(c) inversion temperature
(d) normal temperature
Answer:
(c) Inversion temperature

Question 40.
Which of the following is true about the gaseous state?
(a) Thermal energy = molecular interaction
(b) Thermal energy >> molecular interaction
(c) Thermal energy << molecular interaction
(d) molecular forces >> those in liquids
Answer:
(b) Thermal energy >> molecular interaction

Question 41.
The temperature produced in adiabatic process of liquefaction is …………..
(a) zero kelvin
(b) -273 K
(c) 10-4 K
(d) 104 K
Answer:
(c) 10-4 K

Question 42.
Gas deviates from ideal gas nature because molecules
(a) are colourless
(b) attract each other
(c) contain covalent bond
(d) show Brownian movement
Answer:
(b) attract each other

Question 43.
The compressibility factor for an ideal gas is …………….
(a) 1.5
(b) 2
(c) 1
(d) x
Answer:
(c) 1

Question 44.
Which of the following pair will diffuse at the same rate?
(a) CO2 and N2O
(b) CO2 and NO
(c) CO2 and CO
(d) N2O and NO
Answer:
(a) CO2 and N2O

Question 45.
What are the most favourable conditions to liquefy a gas?
(a) High temperature and low pressure
(b) Low temperature and high pressure
(c) High temperature and high pressure
(d) Low temperature and low pressure
Answer:
(b) Low temperature and high pressure

Question 46.
A person living in Shimla observed that cooking food with using pressure cooker takes more time. The reason for this observation is that at high altitude …………..
(a) pressure increases
(b) temperature decreases
(c) pressure decreases
(a) temperature decreases
Answer:
(c) pressure decreases

Question 47.
Statement-I: At constant temperature PV vs V plot for real gases is not a straight line.
Statement-II : At high pressure, all gases have Z >1, but at intermediate pressure most gases have Z <1.
(a) Statement-I and II are correct and Statement-II is the correct explanation of Statement-I
(b) Statement-I and II are correct but Statement-II is not the correct explanation of Statement-I
(c) Statement-I is correct but Statement-Il is wrong
(d) Statement-I is wrong but Statement-Il is correct .
Answer:
(a) Statement-I and II are correct and Statement-II is the correct explanation of Statement-I

Question 48.
Statement-I: Gases do not liquefy above their critical temperature, even on applying high press ure.
Statement-II: Above critical temperature, the molecular speed is high and intermolecular
attractions cannot hold the molecules together because they escape because of high speed.
(a) Statement-I and II are correct and Statement-II is the correct explanation of Statement-I
(b) Statement-I and II are correct but Statement-II is not the correct explanation of Statement-I
(c) Statement-I is correct but Statement-II is wrong
(d) Statement-I is wrong but Statement-II is correct
Answer:
(c) Statement-I and II are correct and Statement-IIs the correct explanation of Statement-I

Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State

Question 49.
NH3 gas is liquefied more easily than N2. Hence
(a) Van der Waals constant a and b of NH3 > that of N2
(b) van der Waals constants a and b of NH3 < that of N2
(c) a(NH3) > a(N2) but b(NH3) < b(N2)
(d) a(NH3) < a(N2) but b(NH3) > b(N2)
Answer:
(c) a(NH3) > a(N2) but b(NH3) < b(N2)

Question 50.
In a closed flask of 5 liters, 1.0 g of H2 is heated from 300 to 600 K, which statement is not correct’?
(a) pressure of the gas increases
(b) the rate of the collusion increase
(c) the number of moles of gas increases
(d) the energy of gaseous molecules increases
Answer:
(c) the number of moles of gas increases

Question 51.
Match the List-I and List-II using the correct code given below the list.
Samacheer Kalvi 11th Chemistry Solutions Chapter 3 Periodic Classification of Elements - 49
Answer:
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State

Question 52.
Consider the following statements.
(i) All the gases have higher densities than liquids and solids.
(ii) All gases occupy zero volume at absolute zero.
(iii) At very low pressure all gases exhibit ideal behaviour.
Which of the above statement is/are not correct?
(a) (i) only
(b) (ii) only
(c) (iii) only
(d) (ii) and (iii) only
Answer:
(a) (i) only

Question 53.
Which of the following gas is present maximum in atmospheric air?
(a) O2
(b) N2
(c) H2
(d) radon
Answer:
(b) N2

Question 54.
Which law is used in the process of enriching the isotope of U235 from other isotopes?
(a) Boyle’s law
(b) Dalton’s law of partial pressure
(c) Graham’s law of diffusion
(d) Charles’ law
Answer:
(c) Graham’s law of diffusion

Samacheer Kalvi 11th Chemistry Gaseous State 2 – Mark Questions

Question 1.
Define Pressure? Give its unit?
Answer:
Pressure is defined as force divided by the area to which the force is applied. The SI unit of pressure is pascal which is defined as 1 Newton per square meter (Nm-2).
Pressure = \(\frac{\text { Force }\left(\mathrm{N}(\text { or }) \mathrm{Kg} \mathrm{ms}^{-2}\right)}{\text {Area }\left(\mathrm{m}^{2}\right)}\)

Question 2.
Distinguish between a gas and a vapour.
Answer:

  • Gas: A substance that is normally in a gaseous state at ordinary temperature and pressure. e.g., Hydrogen.
  • Vapour: The gaseous form of any substance that is a liquid or solid at normal temperature and pressure. e.g., At 298 K and 1 atm, water exist as water vapour.

Question 3.
State Dalton’s law of partial pressure.
Answer:
The total pressure of a mixture of non-reacting gases is the sum of partial pressures of the gases present in the mixture” where the partial pressure of a component gas is the pressure that it would exert if it were present alone in the same volume and temperature. This is known as Dalton s law of partial pressures.
For a mixture containing three gases 1, 2, and 3 with partial pressures p1, p2, and p3 in a container with volume V, the total pressure Ptotal will be given by
Ptotal = p1 + p2 + p3

Question 4.
Define atmospheric pressure. What is its value?
Answer:

  • The pressure exerted on a unit area of Earth by the column of air above it is called atmospheric pressure.
  • The standard atmospheric pressure = 1 atm.
  • 1 atm = 760 mm Hg.

Question 5.
Define the Critical temperature (Tc) of a gas?
Answer:
Critical temperature (Tc) of a gas is defined as the temperature above which it cannot be liquefied even at high pressure.

Question 6.
Most aeroplanes cabins are artificially pressurized. Why?
Answer:
The pressure decreases with the increase in altitude because there are fewer molecules per unit volume of air. Above 9200 m (30,000 ft), for example, where most commercial aeroplanes fly, the pressure is so low that one could pass out for lack of oxygen. For this reason most aeroplanes cabins arc artificially pressurized.

Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State

Question 7.
How do you understand the PV relationship?
Answer:
The PV relationship can be understood as follows. The pressure is due to the force of the gas particles on the walls of the container. If a given amount of gas is compressed to half of its volume, the density is doubled and the number of particles hitting the unit area of the container will be doubled. Hence, the pressure would increase twofold.

Question 8.
State Charles’ law.
Answer:
Charles’ law:
For a fixed mass of a gas constant pressure, the volume is directly proportional to temperature (K).
Mathematically V – T at constant P and n. (or) \(\frac {V}{T}\) = Constant (or) \(\frac{V_{1}}{T_{1}}=\frac{V_{2}}{T_{2}}\) = Constant

Question 9.
A gas cylinder can withstand a pressure of 15 aim. The pressure of the cylinder is measured 12 atm at 27°C. Upto which temperature limit the cylinder will not burst?
Answer:
Cylinder will burst at that temperature when it attains the pressure of 15 atm
P1 = 12 atm
T = 27° C = (27 + 273)K = 300K
P2 = 15 atm; T = ?
\(\frac{P_{1}}{T_{1}}=\frac{P_{2}}{T_{2}}\)

T2 = \(\frac{15 \times 300}{12}\) = 375 K
= (375 – 273)°C = 102°C

Question 10.
State Avogadro’s hypothesis.
Answer:
Equal volumes of all gases under the same conditions of temperature and pressure contain equal number of molecules. Mathematically V ∝ n
\(\frac{V_{1}}{n_{1}}=\frac{V_{2}}{n_{2}}\) = Constant

Question 11.
State Charles law.
Answer:
For a fixed mass of a gas at constant pressure, the volume is directly proportional to its temperature.
\(\frac{V}{T}\) = constant (at constant pressure)

Question 12.
What are the applications of Dalton’s law of partial pressure?
Answer:
1. Physicians report the pressure of the patient’s gases in blood, analyzed by hospital lab, the values are reported as partial pressures.
Gas – Normal range
PCO2 35 – 45mm of Hg
PO2  80 – 100 mm of Hg

2. When gas is collected by downward displacement of water, the pressure of dry vapour collected is computed using Dalton’s law
Samacheer Kalvi 11th Chemistry Solutions Chapter 3 Periodic Classification of Elements - 50

Question 13.
How can you identify a heavy smoker with the help of Dalton’s law?
Answer:
Physicians report the pressure of the patient’s gases in blood, analyzed by hospital lab. The values are reported as partial pressures.
Samacheer Kalvi 11th Chemistry Solutions Chapter 3 Periodic Classification of Elements - 51
A heavy smoker may be expected to have low O2 and huge CO2 partial pressures.

Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State

Question 14.
State Gay-Lussac law.
Answer:
At constant volume, the pressure of a fixed mass of a gas is directly proportional to temperature.
P ∝ T (at constant volume)

Question 15.
Helium diffuses more than air. Give reason.
Answer:
Take two balloons, one is filled with air and another with helium. After one day, the helium balloon was shrunk, because helium being lighter diffuses out faster than the air

Question 16.
Distinguish between diffusion and effusion.
Answer:
The property of gas that involves the movement of the gas molecules through another gas is called diffusion. Effusion is another process in which a gas escapes from a container through a very small hole.

Question 17.
What is the compression factor?
Answer:
The deviation of real gases from ideal behaviour is measured in terms of a ratio of PV to nRT.
This is termed as a compression factor.
Compression factor = Z = \(\frac {PV}{nRT}\)
For ideal gases Z = 1 at all temperatures and pressures.

Question 18.

  1. Define critical temperature.
  2. What is the critical temperature of CO2 gas?

Answer:

  1. The temperature below which a gas can be liquefied by the application of pressure is known as critical temperature.
  2. The critical temperature of CO2 gas is 303.98 K.

Question 19.

  1. Define critical pressure.
  2. What is the critical pressure of CO2 gas?

Answer:

  1. Critical temperature (PC) of a gas is defined as the minimum pressure required to liquefy.
  2. The critical pressure of CO2 is 73 atm.

Question 20.
CO2 gas cannot be liquefied at room temperature. Give reason.
Answer:
Only below the critical temperature, by the application of pressure, a gas can be liquefied. CO2 has critical temperature as 303.98 K. Room temperature means (30 + 273 K) 3O3 K. At room temperature, (critical temperature) even by applying large amount of pressure CO2 cannot be liquefied. Only below the critical temperature, it can be liquefied. At room temperature, CO2 remains as gas.

Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State

Question 21.
What is meant by the Joule-Thomson effect?
Answer:
The phenomenon of lowering of temperature when a gas is made to expand adiabatically form a region of high pressure into a region of low pressure is known as Joule-Thomson effect.

Question 22.
Define inversion temperature.
Answer:
The temperature below which a gas obey Joule-Thomson effect is called inversion temperature (Ti).
Ti = \(\frac {2a}{Rb}\)

Question 23.
State and explain Boyle’s law. Represent the law graphically.
Answer:
It states that, the pressure of a fixed mass of a gas is inversely proportional to its volume if temperature is kept constant.
P – \(\frac {1}{V}\)
PV = Constant (n and T are constant)
P1v1 = P2V2
Graphical Representation:
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State

Question 24.
Give an expression for the van der Waals equation. Give the significance of the constants used in the equation. What are their units?
Answer:
\(\left(P+\frac{n^{2} a}{V^{2}}\right)\) (V- nb) = nRT
Where n is the number of moles present and ‘a’’ b’ are known as van der Waals constants.

Significance of Van der Waals constants:
Van der Waals constant ‘a’:
‘a’ is related to the magnitude of the attractive forces among the molecules of a particular gas. Greater the value of ’a’, more will be the attractive forces.
Unit of ’a’ = L2 mol-2

Van der Waals constant ‘b’:
‘b’ determines the volume occupied by the gas molecules which depends upon size of molecule.
Unit of ‘b’ = L mol-1

Question 25.
What are ideal and real gases? Out of CO2 and NH3 gases, which is expected to show more deviation from the ideal gas behaviour?
Answer:
Ideal gas:
A gas that follows Boyle’s law, Charles’ law and Avogadro law strictly is called an ideal gas. It is assumed that intermolecular forces are not present between the molecules of an ideal gas.

Real gases:
Gases which deviate from ideal gas behaviour are known as real gases. NH3 is expected to show more deviation. Since NH3 is polar in nature and it can be liquefied easily.

Samacheer Kalvi 11th Chemistry Gaseous State 3 – Mark Questions

Question 1.
Explain the graphical representation of Boyle’s law.
Answer:
Boyle’s law states that at a given temperature the volume occupied by a fixed mass of a gas is inversely proportional to its pressure. V ∝ (T and n are fixed).
If the pressure of the gas increases, the volume will decrease and if the pressure of the gas decreases, the volume will increase. So PV = Constant.
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State

Question 2.
What are the different methods of liquefaction of gases?
Answer:
There are different methods used for the liquefaction of gases:

  1. In Linde’s method, the Joule-Thomson effect is used to get liquid air or any other gas.
  2. In Claude’s process, the gas is allowed to perform mechanical work in addition to the Joule-Thomson effect so that more cooling is produced.
  3. In the Adiabatic process, cooling is produced by removing the magnetic property of magnetic material such as gadolinium sulphate. By this method, a temperature of 10-4 K i.e., as low as 0 K can be achieved.

Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State

Question 3.
Explain Charles’ law with an experimental illustration.
Answer:
Charles’ law states that for a fixed mass of a gas at constant pressure, the volume is directly proportional to temperature (K).
V ∝ T (or) \(\frac {V}{T}\) = Constant
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State

Volume vs Temperature:
If a balloon is moved from an ice water bath to a boiling water bath, the gas molecules inside move faster due to increased temperature and hence the volume increases.

Question 4.
Explain the graphical representation of Charles’ law.
Answer:
1. Variation of volume of the gas sample with temperature at constant pressure.
2. Each line (iso bar) represents the variation of volume with temperature at certain pressure. The pressure increases from P1 to P5.
3.  i.e. P1<P2 < P3  <P4 < P5 . When these lines are extrapolated to zero volume, they intersect at a temperature of -273.15°C.
4. All gases are becoming liquids, if they are cooled to sufficiently low temperatures.
5. In other words, all gases occupy zero volume at absolute zero. So the volume of a gas can be measured over only a limited temperature range.
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State

Question 5.
Explain graphicl representation of Gay Lussac’s law
Answer:
Gay Lussac’s law
At constant volume, the pressure of a fixed mass of a gas is directly proportional to temperature.
P – T (or) \(\frac {P}{T}\) = Constant
It can be graphically represented as shown here:
Lines in the pressure vs temperature graph are known as isochores (constant volume) of a gas.
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State

Question 6.
Explain the graphical representation of Avogadro’s hypothesis.
Answer:
Avogadro’s hypothesis states that equal volumes of all gases under the same conditions of temperature and pressure contain equal number of molecules.
V ∝ n
\(\frac{V_{1}}{n_{1}}=\frac{V_{2}}{n_{2}}\) = Constant.
Where V1 and are the volume and number 10- of moles of a gas and V2 and n2 are the different set of values of volume and number of moles of the same gas.

Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State

A better example to illustrate Avogadro’s Number of Moles (n) hypothesis is to observe the effect of pumping more gas into a balloon. When more gas molecules (particularly CO2) are passed, the volume of the balloon increases. The pressure and temperature stay constant as the balloon inflates, so the increase in volume is due to the increase in the quantity of gas inside the balloon.

Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State

Question 7.
The vapour pressure of water at 80°C is 355.5 mm of Hg. A 100 mL vessel contains water saturated with O2 at 80°C, the total pressure being 760 mm of Hg. The contents of the vessel were pumped into a 50 mL vessel at the same temperature. What is the partial pressure of O2?
Answer:
Ptotal = PH2O + PO2
PO2 = 760 – 355.5 = 404.5
When the contents were pumped into 50 mL vessel
P1 = 404.5
V1 = 100 mL
P2 =?
V2 = 50 mL
P1V1 = P2V2
P2 = \(\frac{404.5 \times 100}{50}\) = 809 mm
Thus, PO2 in 50 mL vessel = 809 mm

Question 8.
Derive the various values of R, gas constant.
Answer:
1. For standard conditions in which P is 1 atm, volume 22.4 14 dm3 for 1 mole at 273.15 K.
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State
= 0.08205 7 dm3 atm mol-1 K-1

2. Where P = 105 Pascal, V = 22.71 x 10-3 m3 for I mole of a gas at 273.15 K.
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State
= 8.314 pa m3 K-1 mol-1
=8.314x 10-2bar dm3 K-1mol-1
R = 8.314 J K-1 mol-1.

Question 9.
What is meant by Boyle’s temperature (or) Boyle’s point? How is it related to the compression point?
Answer:
(1) Over a range of low pressures, the real gases can behave ideally at a particular temperature called as Boyle temperature or Boyle point.
(2) The Boyle point varies with the nature of the gas.
(3) Above the Boyle point, the compression point Z > 1 for real gases i.e. real gases show positive deviation.
(4) Below the Boyle point, the real gases first show a decrease for Z, reaches a minimum and then increase with increase in pressure. So, it is clear that at low pressure and at high temperatures, the real gases behave as ideal gases.
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State

Question 10.
State and explain Dalton’s law of partial pressure.
Answer:
John Dalton stated that “the total pressure of a mixture of non-reacting gases is the sum of partial pressures of the gases present in the mixture” where the partial pressure of a component gas is the pressure that it would exert if it were present alone in the same volume and temperature. This is known as Dalton’s law of partial pressures, i.e., for a mixture containing three gases 1, 2, and 3 with partial pressures p1, p2, and p3 in a container with volume V, the total pressure Ptotal will be given by P = p1 + p2 + p3

Samacheer Kalvi 11th Chemistry Gaseous State 5 – Mark Question

Question 1.
How CH4 He and NH3 are deviating from ideal behaviour? (or) Explain how real gases deviate from ideal behaviour.
Answer:
1. The gases which obey gas equation PV = nRT are known as ideal gases. The gases which do not obey PV = nRT are known as real gases.

2. The gas laws and the kinetic theory are based on the assumption that molecules in the gas phase occupy negligible volume (assumption 1) and that they do not exert any force on one another either attractive or repulsive (assumption 2). Gases whose behaviour is consistent with these assumptions are said to exhibit ideal behaviour.

3. The following graph shows RT plotted against P for three real gases and an ideal gas at a given temperature.

4. According to ideal gas equation, PV/RT is equal to n. Plot PV/RT versus P for ‘n’ moles oigas at 0°C. For1 mole of an ideal gas PV/ RT is equal to 1 irrespective of the pressure of the gas.

5. For real gases, we observe various deviations from ideal behaviour at high pressure. At very low pressure, all gases exhibit ideal behaviour, ie. PV/RT values all converge to n as P approaches zero.
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State
6. For real gases, this is true only at moderate low pressures. (≤ 5 atm) significant variation occurs as the pressure increases. Attractive forces operate among molecules at relatively short deviation.

7. At atmospheric pressure, the molecules in a gas are far apart and attractive forces arc negligible. At high pressure, the density of the gas increases and the molecules are much closer to one another. Intermolecular forces can be significant enough to affect the motion of the molecules and the gas will not behave ideally.

Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State

Question 2.
Derive Van der Waals equation of state.
Answer:
1. Consider the effect of intermolecular forces on the pressure exerted by a gas form the following explanation.

2. The speed of a molecule that is moving toward the wall of a container is reduced by the attractive forces exerted by its neighbours. Hence, the measured gas pressure is Q lower than the pressure the gas would exert, if it behave ideally.
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State
Where ‘a’ is the proportionality constant and depends on the nature of the gas and n and V are the number of moles and volume of the container and respectively an2/ V2 is the correction term.

3. The frequency of encounters increases with the square of the number of molecules per unit volume n2/ V2. Therefore an2/ V2 represents the intermolecular interaction that causes non-ideal behaviour.

4.  Another correction is concerned with the volume ¿ccupied by the gas molecules. ‘V’ represents the volume of the container. As every individual molecule of a real gas occupies certain volume, the effective volume V- nb which is the actually available for the gas, n is the number of moles and b is a constant of gas.

5.  Hence Van der Waals equation of state for real gases are given as \(\left(P+\frac{a n^{2}}{V^{2}}\right)\) (V – nb) = nRT Where a and b are Van der Waals constants.

Question 3.
Explain about Andrew’s experimental isotherms of CO2 gas.
Answer:
1. Andrew plotted isotherms of carbon dioxide at different temperatures. it is then proved that many real gases behave in a similar manner like CO2.

2. At a temperature of 303.98 K, CO2 remains as a gas. Below this temperature, CO2, turns into liquid CO2 at 7 3atm. It is called the critical temperature of CO2.
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State

3. At 303.98 K and 73 atm pressure, CO3,, becomes a liquid but remains a gas at higher temperature.

4. Below the critical temperature, the behaviour of CO2 is different. For example, consider an isotherm of CO2 at 294.5 K, it is a gas until the point B, is reached. At B, a liquid separates along the line BC, both the liquid and gas co-exist. At C, the gas is completely condensed.

5. If the pressure is higher than at C, only the liquid is compressed so, a steep rise in pressure is observed. Thus, there exist a continuity of state.

6.  A gas below the critical temperature can be liquefied by applying pressures.

Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State

Activity – 1
The table below contains the values of pressure measured at different temperatures for 1 moie of an ideal gas. Plot the values in a graph and verify the Gay Lussac’s law. [Lines in the pressure vs temperature graph are known as iso chores (constant volume) of a gas]
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State
Solution:
Gay Lussac’s law at constant volume = \(\frac{P_{1}}{T_{1}}=\frac{P_{2}}{T_{2}}\)
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State
If temperature increases, pressure also increases.
So \(\frac{P_{1}}{T_{1}}=\frac{P_{2}}{T_{2}}\)
Samacheer Kalvi 11th Chemistry Solutions Chapter 6 Gaseous State

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Samacheer Kalvi 11th Economics Solutions Chapter 7 Indian Economy

Students can Download Economics Chapter 7 Indian Economy Questions and Answers, Notes Pdf, Samacheer Kalvi 11th Economics Book Solutions Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 11th Economics Solutions Chapter 7 Indian Economy

Samacheer Kalvi 11th Economics Indian Economy Text Book Back Questions and Answers

MCQ Questions for Class 11 Hindi with Answers – NCERT Solutions.

Part – A

Multiple Choice Questions

Question 1.
The main gold mine region in Karnataka is _________
(a) Kolar
(b) Ramgiri
(c) Anantpur
(d) Cochin
Answer:
(a) Kolar

Question 2.
The economic growth of a country is measured by national income indicated by _________
(a) GNP
(b) GDP
(c) NNP
(d) Per capita income
Answer:
(b) GDP

Samacheer Kalvi 11th Economics Solutions Chapter 7 Indian Economy

Question 3.
Which one of the following are developed nations?
(a) Mexico
(b) Ghana
(c) France
(d) SriLanka
Answer:
(c) France

Question 4.
The position of the Indian Economy among the other strongest economies in the world is _______
(a) Fourth
(b) Seventh
(c) Fifth
(d) Tenth
Answer:
(b) Seventh

Question 5.
Mixed economy means _________
(a) Private sectors and banks
(b) Co-existence of Public and Private sectors
(c) Public sectors and banks
(d) Public sectors only
Answer:
(b) Co-existence of Public and Private sectors

Question 6.
The weakness of Indian Economy is _________
(a) Economic disparities
(b) Mixed economy
(c) Urbanisation
(d) Adequate employment opportunities
Answer:
(a) Economic disparities

Question 7.
A scientific study of the characteristics of population is _________
(a) Topography
(b) Demography
(c) Geography
(d) Philosophy
Answer:
(b) Demography

Samacheer Kalvi 11th Economics Solutions Chapter 7 Indian Economy

Question 8.
The year 1961 is known as _________
(a) Year of the small divide
(b) Year of Population Explosion
(c) Year of Urbanisation
(d) Year of Great Divide
Answer:
(b) Year of Population Explosion

Question 9.
In which year the population of India crossed the one billion mark?
(a) 2000
(b) 2001
(c) 2005
(d) 1991
Answer:
(b) 2001

Question 10.
The number of deaths per thousand population is called as ________
(a) Crude Death Rate
(b) Crude Birth Rate
(c) Crude Infant Rate
(d) Maternal Mortality Rate
Answer:
(a) Crude Death Rate

Question 11.
The number of births per thousand population is called as _________
(a) Crude death rate
(b) Mortality rate
(c) Morbidity rate
(d) Crude Birth Rate
Answer:
(d) Crude Birth Rate

Samacheer Kalvi 11th Economics Solutions Chapter 7 Indian Economy

Question 12.
Density of population = _________
(a) Land area / Total Population
(b) Land area / Employment
(c) Total Population / Land area of the region
(d) Total Population
Answer:
(c) Total Population / Land area of the region

Question 13.
Who introduced the National Development Council in India?
(a) Ambedkar
(b) Jawaharlal Nehru
(c) Radhakrishanan
(d) V.K.R.V. Rao
Answer:
(b) Jawaharlal Nehru

Question 14.
Who among the following propagated Gandhian Economic thinkings.
(a) Jawaharlal Nehru
(b) VKRV Rao
(c) JC Kumarappa
(d) A.K.Sen
Answer:
(c) JC Kumarappa

Question 15.
The advocate of democratic socialism was
(a) Jawaharlal Nehru
(b) P.C. Mahalanobis
(c) Dr. Rajendra Prasad
(d) Indira Gandhi
Answer:
(a) Jawaharlal Nehru

Question 16.
Ambedkar the problem studied by in the context of Indian Economy is ________
(a) Small land holdings and their remedies
(b) Problem of Indian Currency
(c) Economics of socialism
(d) All of them
Answer:
(b) Problem of Indian Currency

Question 17.
Gandhian Economics is based on the Principle _________
(a) Socialistic idea
(b) Ethical foundation
(c) Gopala Krishna Gokhale
(d) Dadabhai Naoroji
Answer:
(b) Ethical foundation

Samacheer Kalvi 11th Economics Solutions Chapter 7 Indian Economy

Question 18.
V.K.R.V Rao was a student of _________
(a) J.M. Keynes
(b) Colin Clark
(c) Adam smith
(d) Alfred Marshal
Answer:
(a) J.M. Keynes

Question 19.
Amartya Kumara Sen received the Nobel prize in Economics in the year.
(a) 1998
(b) 2000
(c) 2008
(d) 2010
Answer:
(a) 1998

Question 20.
Thiruvalluvar economic ideas mainly dealt with _________
(a) Wealth
(b) Poverty is the curse in the society
(c) Agriculture
(d) All of them
Answer:
(d) All of them

Part – B
Answer the following questions in one or two sentences

Question 21.
Write the meaning of Economic Growth.
Answer:

  1. Economic growth is usually measured by National Income, indicated by Gross Domestic Product. [GDP],
  2. The GDP is the total monetary value of the goods and services produced by that country over a specific period of time, usually one year.
  3. On the basis of the level of economic development, nations are classified as developed and developing economies.

Question 22.
State any two features of a developed economy.
Answer:

  1. High National Income
  2. High per capita Income

Question 23.
Write the short note on natural resources
Answer:

  1. Any stock or reserve that can be drawn from nature is a Natural Resources.
  2. The major natural resources are – land, forest, water, mineral, and energy.
  3. India is rich in natural resources, but the majority of the Indians are poor.
  4. Nature has provided with diverse climate, several rivers for irrigation and power generation, rich minerals, rich forest, and diverse soil.

Question 24.
Point out anyone feature of Indian Economy
Answer:
Indian economy is a mixed economy. In India, both the private and public sectors coexist.

Question 25.
Give the meaning of non-renewable energy
Answer:
Non-renewable energy sources

  1. The sources of energy which cannot be renewed or re-used are called non-renewable energy sources.
  2. Basically, these are the energy sources that will get exhausted over a period of time.
  3. Some of the examples of this kind of resources are coal, oil, gas, etc.

Samacheer Kalvi 11th Economics Solutions Chapter 7 Indian Economy

Question 26.
Give a short note on Sen’s ‘Choice of Technique’.
Answer:
In a labour surplus economy, the generation of employment cannot be increased at the initial stage by the adaptation of capital intensive technique what’s called the choice of technique.

Question 27.
List out the reasons for low per capita income as given by V.K.R.V. Rao.
Answer:

  1. Uneconomic holdings with sub-divisions and fragmentation.
  2. Low levels of water availability for crops.
  3. Excess population pressure on agriculture due to the absence of a large industrial sector.
  4. Absence of capital.
  5. Absence of autonomy in currency policy, and in general in monetary matters encouraging holding of gold.

Part – C
Answer the following questions in One Paragraph

Question 28.
Define Economic Development.
Answer:
The level of economic development is indicated not just by GDP, but by an increase in citizen’s quality of life or well-being. The quality of life is being assessed by several indices such as the Human Development Index (HDI), Physical Quality of Life Index (PQLI), and Gross National Happiness Index (GNHI)

Question 29.
State Ambedkar’s Economic ideas on agricultural economics.
Answer:
In thel918, Ambedkar published a paper “Small Holding in India and their Remedies”. Citing Adam Smith’s “Wealth of Nations”, he made a fine distinction between “Consolidation of Holdings” and Enlargement of Holdings”.

Question 30.
Write on the short note on village Sarvodaya.
Answer:
Village Sarvodaya is the concept of Gandhiji on the development of villages. To Gandhi, India lives in villages. He was interested in developing the villages as self-sufficient units.

According to him, “Real India was to be found in villages and not in towns or cities”.
So he suggested the development of self-sufficient, self-dependent villages.

Samacheer Kalvi 11th Economics Solutions Chapter 7 Indian Economy

Question 31.
Write the strategy of Jawahar lal Nehru in India’s planning.
Answer:

  1. Jawaharlal Nehru was responsible for the introduction of planning in our country.
  2. To Jawaharlal Nehru, the Plan was essentially an integrated approach for development.
  3. Initiating the debate on the Second Plan in the Lok Sabha in May 1956, Nehru spoke on the theme of planning.
  4. Nehru Said, “the essence of planning is to find the best way to utilize all resources of manpower, of money and so on”.
  5. Planning for Nehru was essentially linked up with industrialization and eventual self-reliance for the country’s economic growth on a self-accelerating growth.
  6. Nehru carried through this basic strategy of planned development.

Question 32.
Write the V.K.R.V.Rao’s contribution to the multiplier concept.
Answer:

  1. Rao’s examination of the “interrelation between investment, income and multiplier in an underdeveloped economy (1952)” was his major contribution to macroeconomic theory.
  2. In it, he asserts that the Keynesian multiplier principle remains inoperative in underdeveloped countries.
  3. V.K.R.V. Rao was the best equipped of all Keynes’ pupils.

Question 33.
Write a short note on Welfare Economics given by Amartya Sen.
Answer:

  1. Amartya Kumar Sen has included the concept of entitlement items like nutrition, food, medical and health care, employment, the security of food supply in times of famine, etc.
  2. He considered famine as arising out of the failure of establishing a system of entitlements.

Samacheer Kalvi 11th Economics Solutions Chapter 7 Indian Economy

Question 34.
Explain Social infrastructure.
Answer:

  1. Social infrastructure refers to those structures which are improving the quality of man power and contribute indirectly towards the growth of an economy.
  2. These structures are outside the system of production and distribution.
  3. The development of these social structures help in increasing the efficiency and productivity of man power.
    (Eg.) Schools, Colleges, Hospitals

Part – D
Answer the following questions in about a page

Question 35.
Explain strong features Indian economy
Answer:
Strengths of Indian Economy:
1. India has a mixed economy:

  • Indian economy is a typical example of mixed economy.
  • This means both private and public sectors co-exist and function smoothly.
  • The fundamental and heavy industrial units are being operated under the public sector.
  • Due to the liberalization of the economy, the private sector has gained importance.
  • This makes it a perfect model for public-private partnership.

2. Agriculture plays the key role:

  • Agriculture being the maximum pursued occupation in India.
  • It plays an important role in its economy as well.
  • Around 60% of the people in India depend upon agriculture for their livelihood.
  • In fact, about 17% of our GDP today is contributed by the agriculture sector.
  • Green revolution, ever green revolution and inventions is bio technology have made agriculture self sufficient and also surplus production.
  • The export of agricultural products such as fruits, vegetables, spices, vegetable oils, tobacco, animal skin, etc. also add to forex earning through international trading.

3. An emerging market:

  • Indian has emerged as vibrant economy sustaining stable GDP growth rate even in the midst of global downtrend.
  • This has attracted significant foreign capital through FDI and FII.
  • India has a high potential for prospective growth.
  • This also makes it an emerging market for the world.

4. Emerging Economy:

  • Emerging as a top economic giant among the world economy.
  • India bags the seventh position in terms of nominal Gross Domestic Product [GDP] and third in terms of Purchasing Power Parity [PPP].
  • As a result of rapid economic growth, Indian economy has a place among the G20 countries.

5. Fat Growing Economy:

  • Indians economy is well known for high and sustained growth.
  • It has emerged as the world’s fastest growing economy in the year 2016-17 with the growth rate of 7.1 % in GDP.

6. Fast Growing Service Sector:

  • The service sector, contributes a lion’s share of the GDP in India.
  • There has been a high rise growth in the technical sectors like information technology.

7. Large Domestic Consumption:

  • With the faster growth rate in the economy the standard of living has improved a lot.
  • The standard of living has considerably improved and life style has changed.

8. Rapid Growth of Urban Areas:

  • Urbanization is a key ingredient of the growth of any economy.
  • Improved connectivity is transport and communication, education and health have speeded up the pace of urbanization.

9. Stable Macro Economy:

  • The Indian economy has been projected and considered as one of the most stable economies of the world.
  • The current year’s Economic survey represents the Indian economy to be a “heaven of macroeconomic stability, resilience and optimism”.

10. Demographic dividend:

  • This means that India is a pride owner of the maximum percentage of youth.
  • The young population is not only motivated but skilled and trained enough to maximize ‘ the growth.
  • Thus human capital plays a key role in maximizing the growth prospects is the country.
  • This has invited foreign investments to the country and outsourcing opportunities too.

Question 36.
Write the importance of mineral resources in India.
Answer:

  1. Iron-ore : Hematite iron is mainly found in Chattisgarh, Jharkhand, Odisha, Goa and Karnataka. Magnetite is found in Western Coast of Karnataka. Some deposits of iron ore are also found in Kerala, Tamil Nadu and Andhra Pradesh.
  2. Coal and Lignite : India ranks third in the coal production. The main centres are West-Bengal, Bihar, Madhya Pradesh, Maharashtra, Odisha and Andhra Pradesh. Bulk production comes from Bengal-Jharkhand coal fields. Lignite is found in Neyveli in Tamil Nadu.
  3. Bauxite : Bauxite is a main source of aluminium. Major reserves are found in Odisha and Andhra Pradesh.
  4. Mica : India stand first in sheet mica production. Andhra Pradesh, Jharkhand, Bihar and Rajasthan are major reserves.
  5. Crude Oil : Oil is being explored in India at many places of Assam and Gujarat.
  6. Gold : India possesses only a limited gold reserve.
  7. Diamond: The total reserves of a diamond is estimated at around 4582 carats.

Question 37.
Bring out Jawaharlal Nehru’s contribution to the idea of economic development.
Answer:

  1. Jawaharlal Nehru, one of the chief builders of Modem India, was the first Prime Minister of Independent India.
  2. He was a great patriot, thinker, and statesman.

1. Democracy and Secularism:

  • Jawaharlal Nehru was a firm believer in democracy.
  • He believed in free speech civil liberty, adult franchise and the Rule of Law and Parliamentary democracy.
  • Secularism is another signal contribution of Nehru to india.

2. Planning:

  • Jawaharlal Nehru was responsible for the introduction of planning in our country.
  • Jawaharlal Nehru, the Plan was essentially an integrated approach for development.
  • Nehru Spoke on the theme of planning.
  • He said “the essence of planning is to find the best way to utilize all resources of manpower, of money and so on”.
  • “Planning for Nehru was essentially linked up with Industrialization and eventual self-reliance for the country’s economic growth on a self-accelerating growth.
  • Nehru carried through this basis strategy of planned development.
  • Nehru’s contribution to the advancement of science, research, technology and industrial development cannot be forgotten.
  • It was during is period, many IITs and Research Institutions were established.
  • Nehru always in insited on “ scientific temper”.

Samacheer Kalvi 11th Economics Solutions Chapter 7 Indian Economy

Question 38.
Write a brief note on the Gandhian economic ideas.
Answer:
Gandhian economics is based on ethical foundations.
Salient features of Gandhian economic thought:

  1. Village republics : Gandhi was interested in developing the villages as self-sufficient units.
  2. On machinery : Gandhi described machinery as ‘Great Sin’.
  3. Industrialism : Gandhi considered industrialism as a curse on mankind.
  4. Decentralization : He advocated a decentralized economy.
  5. Village sarvodaya : Gandhi suggested the development of self-sufficient, self-dependent villages.
  6. Bread labour: Gandhi realized the dignity of human labour. Bread labour or body labour was the expression that Gandhi used to mean manual labour.
  7. The doctrine of trusteeship : Trusteeship provides a means of transforming the present capitalist society into an egalitarian one.
  8. On the food problem : Gandhi was against any sort of food controls. Food controls only create artificial scarcity.
  9. On population : Gandhi was in favour of birth control through brahmacharya or self-control.
  10. On prohibition: Gandhi advocated cent percent prohibition.

Samacheer Kalvi 11th Economics Indian Economy Additional Questions and Answers

Part -A
Choose the best options

Question 1.
Third world country __________
(a) India
(b) China
(c) Bangladesh
(d) Srilanka
Answer:
(c) Bangladesh

Question 2.
__________ is the year of great divide.
(a) 1921
(b) 1918
(c) 1943
(d) 1969
Answer:
(a) 1921

Samacheer Kalvi 11th Economics Solutions Chapter 7 Indian Economy

Question 3.
__________ are BIMARU States.
(a) Tamil Nadu, Kerala, Karnataka, Madhya Pradesh
(b) Bihar, Madhya Pradesh, Rajasthan, Uttarpradesh
(c) West Bengal, Himachal Pradesh, Punjab, Delhi
(d) Andhra Pradesh, Odisa, Gujarat, Chattisgarh
Answer:
(b) Bihar, Madhya Pradesh, Rajasthan, Uttarpradesh

Question 4.
In India, Lignite is found in.
(a) New Delhi
(b) Kolkatta
(c) Ranji
(d) Neyveli
Answer:
(d) Neyveli

Question 5.
Indian educational system comprises of __________ stages.
(a) 6
(b) 12
(c) 3
(d) 4
Answer:
(a) 6

Samacheer Kalvi 11th Economics Solutions Chapter 7 Indian Economy

Question 6.
__________ is considered as the best pupil of J.M. Keynes
(a) A.K. Sen
(b) J.C.Kumarappa
(c) V.K.R.V. Rao
(d) Manmohan Singh
Answer:
(c) V.K.R.V. Rao

Question 7.
Indian Railways introduced first wifi facility in __________
(a) Chennai
(b) Calcutta
(c) Bengaluru
(d) Hyderabad
Answer:
(c) Bengaluru

Question 8.
National Harbour board was set up in __________
(a) 1947
(b) 1950
(c) 1948
(d) 1951
Answer:
(b) 1950

Question 9.
A study on poverty and famines and the concept of entitlements and capability development was done by __________
(a) Adamsmith
(b) A.K.Sen
(c) Marshall
(d) V.K.R.V. Rao
Answer:
(b) A.K.Sen

Question 10.
Percapital income is __________
(a) National income / output
(b) National income / population
(c) National income / percapital output
(d) National income / male population
Answer:
(b) National income / population

Question 11.
‘India lives in villages’ said by __________
(a) V.K.R.V. Rao
(b) J.C. Kumarappa
(c) Mahatma Gandhi
(d) Jawaharlal Nehru
Answer:
(c) Mahatma Gandhi

Match the following and choose the answer using the codes given below

Question 1.
Samacheer Kalvi 11th Economics Solutions Chapter 7 Indian Economy
(a) 1 2 3 4
(b) 3 4 2 1
(c) 1 3 4 2
(d) 2 4 3 1
Answer:
(b) 3 4 2 1

Samacheer Kalvi 11th Economics Solutions Chapter 7 Indian Economy

Question 2.
Samacheer Kalvi 11th Economics Solutions Chapter 7 Indian Economy
(a) 4 1 2 3
(b) 3 4 2 1
(c) 2 4 3 1
(d) 1 2 4 3
Answer:
(a) 4 1 2 3

Question 3.
Samacheer Kalvi 11th Economics Solutions Chapter 7 Indian Economy
(a) 4 1 2 3
(b) 1 2 3 4
(c) 4 3 2 1
(d) 2 4 1 3
Answer:
(d) 2 4 1 3

Choose the odd one out

Question 4.
(a) Poverty and famine
(b) Choice of technique
(c) Economics of caste
(d) Concept of capability
Answer:
(c) Economics of caste

Question 5.
(a) Budget by assignment
(b) Budget by assigned revenue
(c) Budget by shared revenues
(d) Budget by fiscal revenues
Answer:
(d) Budget by fiscal revenues

Samacheer Kalvi 11th Economics Solutions Chapter 7 Indian Economy

Question 6.
(a) Net Domestic Product (NDP)
(b) Human Development Index (HDI)
(c) Physical Quality of Life Index (PQLI)
(d) Gross National Happiness Index (GNHI)
Answer:
(a) Net Domestic Product (NDP)

Choose the correct statement

Question 7.
(a) Indian economy is the seventh-largest in the world
(b) Indian economy is a mixed economy
(c) India ranks third in terms of purchasing power parity
(d) The human capital of India is old
Answer:
(d) The human capital of India is old

Question 8.
(a) The annual addition of population in India equals the total population of Australia.
(b) There exists a huge economic disparity in the Indian economy
(c) Kerala has the highest birth rate
(d) Every 6th person in the world is an Indian
Answer:
(c) Kerala has the highest birth rate

Choose the incorrect statement

Question 9.
Samacheer Kalvi 11th Economics Solutions Chapter 7 Indian Economy
Answer:
(b) Demographic transition – (ii) 2001

Question 10.
Samacheer Kalvi 11th Economics Solutions Chapter 7 Indian Economy
Answer:
(c) 1971 – (iii) 1040

Choose the correct statement

Question 11.
(a) Nehru always insisted on scientific temper
(b) Gandhi advocated a centralized economy
(c) Valluvar has recommended an unbalanced budget
(d) V.K.R.V. Rao’s economic thought is coined as Gandhian Economics.
Answer:
(a) Nehru always insisted on scientific temper

Samacheer Kalvi 11th Economics Solutions Chapter 7 Indian Economy

Question 12.
(a) Until 1979, Education in India was in state list
(b) Education in India follows the 10+3 pattern
(c) Sex ratio refers to the number of females per 1000 males.
(d) India ranks fourth in coal production of the world.
Answer:
(c) Sex ratio refers to the number of females per 1000 males.

Analyze the reason for the following 

Question 13.
Assertion (A) : There exists a huge economic disparity in the Indian economy.
Reason (R) : The proportion of income and assets owned by top 10% of Indians goes on increasing.
(a) Both (A) and (R) are true, (R) is the correct explanation of (A)
(b) Both (A) and (R) are true, (R) is the not correct explanation of (A)
(c) (A) is true and (R) are false.
(d) (A) is false, but (R) is true.
Answer:
(a) Both (A) and (R) are true, (R) is the correct explanation of (A)

Question 14.
Assertion (A) : In Kerala, the adult sex ratio is 1084 as on 2011.
Reason (R) : Kerala provides better status to women as compared to other states.
(a) Both (A) and (R) are true, (R) is not the correct explanation of (A)
(b) Both (A) and (R) are true, (R) is the correct explanation of (A)
(c) Both (A) and (R) are false.
(d) None of the above
Answer:
(b) Both (A) and (R) are true, (R) is the correct explanation of (A)

Fill in the blanks with suitable option given below

Question 15.
In India, Lignite is found in _____
(a) New Delhi
(b) Kolkata
(c) Ranji
(d) Neyveli
Answer:
(d) Neyveli

Question 16.
Indian educational system comprises of _____ stages
(a) 12
(b) 3
(c) 6
(d) 4
Answer:
(c) 6

Question 17.
Indian Railways introduced first wifi facility in _____
(a) Chennai
(b) Bengaluru
(c) Calcutta
(d) Hyderabad
Answer:
(b) Bengaluru

Choose the best option 

Question 18.
_____ is considered as the best pupil of J.M. Keynes
(a) A.K. Sen
(b) J.C.Kumarappa
(c) V.K.R.V.Rao
(d) Nehru
Answer:
(c) V.K.R.V.Rao

Samacheer Kalvi 11th Economics Solutions Chapter 7 Indian Economy

Question 19.
Third world country is _____
(a) India
(b) China
(c) Srilanka
(d) Bangladesh
Answer:
(d) Bangladesh

Question 20.
Per capita income is _____
(a) National income / output
(b) National income / population
(c) National income / per capital output
(d) National income / male population
Answer:
(b) National income / population

Part – B
Answer the following questions in one or two sentences 

Question 1.
What is Gross National Happiness Index?
Answer:
GNHI is an indicator of progress, which measures sustainable development, environmental conservation, promotion of culture and good governance.

Question 2.
State any two weaknesses of Indian Economy.
Answer:

  1. Large population.
  2. Inequality and poverty.

Question 3.
What is sex ratio?
Answer:
Sex ratio refers to the number of females per 1,000 males.

Question 4.
Explain economic infrastructure.
Answer:
Economic infrastructure is the support system which helps in facilitating the production

Question 5.
What is Gandhian Economics?
Answer:
J.C. Kumarappa developed economic theories based on Gandhism. He developed a school of economic thought coined as Gandhian Economics.

Question 6.
Which are “BIMARU” states ?
Answer:

  1. Bihar
  2. Madhya Pradesh
  3. Rajasthan
  4. Uttarpradesh

Question 7.
What is year of small divide?
Answer:
In 1951, population growth rate has come down from 1.33% to 1.25%. Hence it is known as year of small divide.

Part – C
Answer the following questions in one Paragraph

Question 1.
What are the aspects of demographic trends in India ?
Answer:

  1. Size of population
  2. Rate of growth.
  3. Birth and death rates
  4. Density of population
  5. Sex – ratio
  6. Life – expectancy at birth
  7. Literacy ratio.

Question 2.
Explain Thiruvalluvar’s ideas on agriculture.
Answer:
According to Thiruvalluvar, agriculture is the most fundamental economic activity. They are the axle-pin of the world, for on their prosperity revolves prosperity of other sectors of the economy. He says, plowmen alone is the freemen of the soil. He believes that agriculture is superior to all other occupations.

Samacheer Kalvi 11th Economics Solutions Chapter 7 Indian Economy

Question 3.
Write short note on Birth rate and Death rate.
Answer:
Short Note On Birth Rate And Death Rate:

  1. Birth Rate : It refers to the number of births per thousand of the population.
  2. Death Rate : It refers to the number of deaths per thousand of the population.

Kerala has the lowest birth rate and Uttarpradesh has the highest birth rate. West Bengal has the lowest and Orissa has the highest death rates.

Part – D
Answer the following questions in about a page

Question 1.
Explain about health in India.
Answer:
Health in India is a state government responsibility. The central council of health and welfare formulates the various health care projects and health department reform policies. The administration of health industry is the responsibility of the ministry of health and welfare.

Health care in India has many forms. But, all medical systems are under one ministry AYUSH.
Health status is better in Kerala as compared to other states. India’s health status is poor compared to Sri Lanka.

Samacheer Kalvi 11th Economics Solutions Chapter 7 Indian Economy

Question 2.
Explain Thiruvalluvar’s economic ideas.
Answer:
The economic ideas of Thiruvalluvar are found in his immortal work, Thirukkural in its second part porutpal.

  1. Factors of production: Thiruvalluvar has made many passing references about the factors of production, land, labour, capital, organization.
  2. Agriculture: Agriculture is the most fundamental economic activity. The prosperity of other sectors depends on the prosperity of agriculture. Valluvar believes that agriculture is superior to all other occupations.
  3. Public finance: He elaborately explained public finance under the headings public revenue, financial administration and public expenditure.
  4. Public expenditure: Valluvar has recommended a balanced budget. He advocates
    • Defence
    •  Public works
    • Social Services
  5. External assistance: Valluvar was against seeking external assistance. He advocated a self-sufficient economy.
  6. Poverty and begging: According to him ‘poverty is the root cause of all other evils which would lead to ever-lasting sufferings.
  7. Wealth: Valluvar has regarded wealth as only a means and not an end.
  8. Welfare state: The important elements of a welfare state are
    • Perfect health of the people without the disease
    • Abundant wealth
    • Good crop
    • Prosperity and happiness
    • Full security for the people.

Samacheer Kalvi 11th Economics Solutions Chapter 7 Indian Economy Read More »

Samacheer Kalvi 11th Bio Botany Solutions Chapter 12 Mineral Nutrition

Students can Download Bio Botany Chapter 12 Mineral Nutrition Questions and Answers, Notes Pdf, Samacheer Kalvi 11th Bio Botany Book Solutions Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 11th Bio Botany Solutions Chapter 12 Mineral Nutrition

Samacheer Kalvi 11th Bio Botany Mineral Nutrition Text Book Back Questions and Answers

Question 1.
Identify correct match.

1. Die back disease of citrus (i) Mo
2. Whip tail disease (ii) Zn
3. Brown heart of turnip (iii) Cu
4. Little leaf (iv) B

(a) 1. (iii), 2. (ii), 3. (iv), 4. (i).
(b) 1. (iii), 2. (i), 3. (iv), 4. (ii).
(c) 1. (i), 2. (iii), 3. (ii), 4. (iv).
(d) 1. (iii), 2. (iv), 3. (ii), 4. (i).
Answer:
(b) 1. (iii), 2. (i), 3. (iv), 4. (ii).

Question 2.
If a plant is provided with all mineral nutrients but, Mn concentration is increased, what will be the deficiency?
(a) Mn prevent the uptake of Fe, Mg but not Ca
(b) Mn increase the uptake of Fe, Mg and Ca
(c) Only increase the uptake of Ca
(d) Prevent the uptake Fe, Mg, and Ca
Answer:
(a) Mn prevent the uptake of Fe, Mg but not Ca

Samacheer Kalvi 11th Bio Botany Solutions 12 Mineral Nutrition

Question 3.
The element which is not remobilized?
(a) Phosphorus
(b) Potassium
(c) Calcium
(d) Nitrogen
Answer:
(c) Calcium

Question 4.
Match the correct combination.

Minerals

Role

(a) Molybdenum 1. Chlorophyll
(b) Zinc 2. Methionine
(c) Magnesium 3. Auxin
(d) Sulphur 4. Nitrogenase

(a) A – 1, B – 3, C – 4, D – 2
(b) A – 2, B – 1, C – 3, D – 4
(c) A – 4, B – 3, C – 1, D – 2
(d) A – 4, B – 2, C – 1, D – 3
Answer:
(c) A – 4, B – 3, C – 1, D – 2

Question 5.
Identify the correct statement:
(i) Sulphur is essential for amino acids Cystine and Methionine
(ii) Low level of N, K, S and Mo affect the cell division
(iii) Non – leguminous plant Alnus which contain bacterium Frankia
(iv) Denitrification carried out by nitrosomonas and nitrobacter.

(a) (i), (ii) are correct
(b) (i), (ii), (iii) are correct
(c) I only correct
(d) all are correct
Answer:
(b) (i), (ii), (iii) are correct

Question 6.
The nitrogen is present in the atmosphere in huge amount but higher plants fail to utilize it. Why?
Answer:
The higher plants do not have the association of bacteria or fungi, which are able to fix atmospheric nitrogen.

Question 7.
Why is that in certain plants deficiency symptoms appear first in younger parts of the plants while in others, they do so in mature organs?
Answer:
In certain plants, the deficiency symptom appears first in the younger part of the plant, due to the immobile nature of certain minerals like calcium, sulphur, iron, boron and copper.

Question 8.
Plant A in a nutrient medium shows whiptail disease plant B in a nutrient medium shows a little leaf disease. Identify mineral deficiency of plant A and B?
Answer:
Mineral deficiency of plant A and B:

  1. Plant A is deficient of the mineral molybdenum (Mo).
  2. Plant B is deficient of the mineral zinc (Zn).

Question 9.
Write the role of nitrogenase enzyme in nitrogen fixation?
Answer:
The role of nitrogenase enzyme in nitrogen fixation:
Samacheer Kalvi 11th Bio Botany Solutions Chapter 12 Mineral Nutrition 2

Question 10.
Explain the insectivorous mode of nutrition in angiosperms?
Answer:
Plants which are growing in nitrogen deficient areas develop insectivorous habit to resolve nitrogen deficiency.
(i) Nepenthes (Pitcher plant): Pitcher is a modified leaf and contains digestive enzymes. Rim of the pitcher is provided with nectar glands and acts as an attractive lid. When insect is trapped, proteolytic enzymes will digest the insect.
Samacheer Kalvi 11th Bio Botany Solutions Chapter 12 Mineral Nutrition 3

(ii) Drosera (Sundew): It consists of long club shaped tentacles which secrete sticky digestive fluid which looks like a sundew.
Samacheer Kalvi 11th Bio Botany Solutions Chapter 12 Mineral Nutrition 4

(iii) Utricularia (Bladder wort): Submerged plant in which leaf is modified into a bladder to collect insect in water.
Samacheer Kalvi 11th Bio Botany Solutions Chapter 12 Mineral Nutrition 5

(iv) Dionaea (Venus fly trap): Leaf of this plant modified into a colourful trap. Two folds of lamina consist of sensitive trigger hairs and when insects touch the hairs it will close.
Samacheer Kalvi 11th Bio Botany Solutions Chapter 12 Mineral Nutrition 6

Samacheer Kalvi 11th Bio Botany Mineral Nutrition Additional Questions & Answers

I. Choose the correct answer (1 Mark)
Question 1.
Plants naturally obtain nutrients from:
(a) atmosphere
(b) water
(c) soil
(d) all of these
Answer:
(d) all of these

Question 2.
Which of the following are included under micro nutrients:
(a) sodium, carbon and hydrogen
(b) magnesium, nitrogen and silicon
(c) sodium, cobalt and selenium
(d) calcium, sulphur and potassium
Answer:
(c) sodium, cobalt and selenium

Question 3.
Who coined the term ‘Hydroponics’:
(a) Julius Von Sachs
(b) William Frederick Goerick
(c) Liebig
(d) Wood word
Answer:
(b) William Frederick Goerick

Question 4.
Selenium is essential for plants:
(a) to prevent water lodging
(b) to enhance growth
(c) to resist drought
(d) to prevent transpiration
Answer:
(a) to prevent water lodging

Question 5.
Actively mobile minerals are:
(a) nitrogen and phosphorus
(b) iron and manganese
(c) sodium and cobalt
(d) silicon and selenium
Answer:
(a) nitrogen and phosphorus

Question 6.
Copper shows deficiency symptoms first that appear in young leaves due to:
(a) less active movement of minerals to younger leaves
(b) active movement of minerals
(c) the immobile nature of mineral
(d) none of the above
Answer:
(c) the immobile nature of mineral

Question 7.
Molybdenum is essential for the reaction of:
(a) hydrolase enzyme
(b) nitrogenase enzyme
(c) carboxylase enzyme
(d) dehydrogenase enzyme
Answer:
(b) nitrogenase enzyme

Question 8.
Match the following:

A. Magnesium (i) dehydrogenase
B. Nickel (ii) ion exchange
C. Zinc (iii) chlorophyll
D. Potassium (iv) urease

(a) A – (ii); B – (i); C – (iv); D – (iii)
(b) A – (iii); B – (ii); C – (i); D – (iv)
(c) A – (ii); B – (iv); C – (i); D – (iii)
(d) A – (iii); B – (iv); C – (i); D – (ii)
Answer:
(d) A – (iii); B – (iv); C – (i); D – (ii)

Question 9.
Nitrogen is the essential component of:
(a) carbohydrate
(b) fatty acids
(c) protein
(d) none of these
Answer:
(c) protein

Question 10.
Which of the element is involved in the synthesis of DNA and RNA:
(a) calcium
(b) magnesium
(c) sulphuric
(d) potassium
Answer:
(b) magnesium

Question 11.
The deficiency of magnesium is the plant, causes:
(a) necrosis
(b) interveinal chlorosis
(c) sand drown of tobacco
(d) all the above
Answer:
(d) all the above

Question 12.
Sulphur is an essential components of amino acids like:
(a) histidine, leucine and aspartic acid
(b) valene, alkaline and glycine
(c) cystine, cysteine and methionine
(d) none of the above
Answer:
(c) cystine, cysteine and methionine

Question 13.
Indicate the correct statements:
(i) Iron is the essential element for the synthesis of chlorophyll and carotenoid
(ii) Iron is the activator of carboxylene enzyme
(iii) Iton is the component of cytochrome
(iv) lvon is the component of plastocyanin

(a) (i) and (ii)
(b) (ii) and (iv)
(c) (ii) and (iii)
(d) (i) and (iii)
Answer:
(d) (i) and (iii)

Question 14.
Khaira disease of rice is caused by:
(a) deficiency of boron
(b) deficiency of zinc
(c) deficiency of iron
(d) deficiency of all the three
Answer:
(b) deficiency of zinc

Question 15.
Match the following:

A. Marginal chlorosis (i) nitrogen
B. Anthocyanin formation (ii) zinc
C. Hooked leaf tip (iii) potassium
D. Little leaf (iv) calcium

(a) A – (ii); B – (iii); C – (i); D – (iv)
(b) A – (iii), B – (ii); C – (iv); D – (i)
(c) A – (iii); B – (i); C – (iv); D – (ii)
(d) A – (iv); B – (iii); C – (i); D – (ii)
Answer:
(c) A – (iii); B – (i); C – (iv); D – (ii)

Question 16.
Increased concentration of manganese in plants will prevent the uptake of:
(a) calcium and potassium
(b) sodium and potassium
(c) boron and silicon
(d) iron and magnesium
Answer:
(d) iron and magnesium

Question 17.
Which of the statement is not correct?
(a) Aluminium toxicity causes the appearance of brown spots in the leaves.
(b) Aluminium toxicity causes the precipitation of nucleic acid.
(c) Aluminium toxicity inhibits ATPase activity
(d) Aluminium toxicity inhibits cell division.
Answer:
(a) Aluminium toxicity causes the appearance of brown spots in the leaves.

Question 18.
The techniques of Aeroponics was developed by:
(a) Goerick
(b) Amon and Hoagland
(c) Soifer Hillel and David Durger
(d) Von Sachs
Answer:
(c) Soifer Hillel and David Durger

Question 19.
Nitrogen occurs in atmosphere in the form of N2, two nitrogen atoms joined together by strong:
(a) di – covalent bond
(b) triple covalent bond
(c) non – valent bond
(d) none of these
Answer:
(b) triple covalent bond

Question 20.
The process of converting atmospheric nitrogen (N2) into ammonia is termed as:
(a) nitrogen cycle
(b) nitrification
(c) nitrogen fixation
(d) ammonification
Answer:
(c) nitrogen fixation

Question 21.
Find out the odd organism:
(a) Rhizobium
(b) Cyanobacteria
(c) Azolla
(d) Pistia
Answer:
(d) Pistia

Question 22.
The legume plants secretes phenolics to attract:
(a) Azolla
(b) Rhizobium
(c) Nitrosomonas
(d) Streptococcus
Answer:
(b) Rhizobium

Question 23.
Which are the organisms help in nitrogen fixation of lichens:
(a) Anabaena and Nostoc
(b) Anabaena alone
(c) Nostoc alone
(d) Anabaena azollae
Answer:
(a) Anabaena and Nostoc

Question 24.
Nitrogenase enzyme is active:
(a) only in aerobic condition
(b) only in anaerobic condition
(c) both in aerobic and anaerobic condition
(d) only in toxic condition
Answer:
(b) only in anaerobic condition

Question 25.
Ammonia (NH3+) is converted into nitrite (NO2) by a bacterium called:
(a) Nitrobacter bacterium
(b) Rhizobium
(c) Anabaena azollae
(d) Nitrosomonas
Answer:
(d) Nitrosomonas

Question 26.
Decomposition of organic nitrogen (proteins and amino acids) from dead plants and animals into ammonia is called:
(a) nitrification
(b) ammonification
(c) nitrogen fixation
(d) denitrification
Answer:
(b) ammonification

Question 27.
The bacteria involved in the denitrification process are:
(a) E.coli and Anabaena
(b) Streptococcus and Bacillus vulgaris
(c) Pseudomonas and Thiobacillus
(d) none of the above
Answer:
(c) Pseudomonas and Thiobacillus

Question 28.
In the process of ammonium assimilation:
(a) Ammonia is converted into nitrites
(b) Ammonia is converted into atmospheric nitrogen
(c) Ammonia is converted into ammonium ions
(d) Ammonia is converted into amino acids
Answer:
(d) Ammonia is converted into amino acids

Question 29.
The transfer of amino group (NH2) from glutamic acid to keto group of keto acid is termed as:
(a) Transamination
(b) Hydrogenation
(c) Nitrification
(d) Denitrification
Answer:
(a) Transamination

Question 30.
Monotrapa (Indian pipe) absorbs nutrients through:
(a) Rhizobium association
(b) mycorrhizal association
(c) microbial association
(d) animal association
Answer:
(b) mycorrhizal association

Question 31.
Cuscuta is a:
(a) partial parasite
(b) total root parasite
(c) obligate stem parasite
(d) partial stem parasite
Answer:
(c) obligate stem parasite

Question 32.
Indicate the correct statement:
(a) Loranthus grows on banana and coconut
(b) Loranthus grows on fig and mango trees
(c) Balanophora is a stem parasite
(d) Viscum is a root parasite
Answer:
(b) Loranthus grows on fig and mango trees

Question 33.
The association of mycorrhizae with higher plants is termed as:
(a) Parasitism
(b) Mutualism
(c) Symbiosis
(d) Saprophytic
Answer:
(c) Symbiosis

Question 34.
In Utricularia, the bladder is a modified form of:
(a) leaf
(b) stem
(c) tentacle
(d) lamina
Answer:
(a) leaf

Question 35.
Lichens are the indicators of:
(a) carbon monoxide
(b) nitrogen oxide
(c) sulphur di oxide
(d) hydrogen sulphide
Answer:
(c) sulphur di oxide

II. Answer the following (2 Marks)

Question 1.
Define micro nutrients of plants.
Answer:
Essential minerals which are required in less concentration called are as Micro nutrients.

Question 2.
Mention any two actively mobile minerals.
Answer:
Nitrogen and Phosphorus.

Question 3.
What is the role of molybdenum in the conversion of nitrogen into ammonia?
Answer:
Molybdenum (Mo) is essential for nitrogenase enzyme during reduction of atmospheric nitrogen into ammonia.

Question 4.
What is the role of potassium on osmotic potential of the cell?
Answer:
Potassium (K) plays a key role in maintaining osmotic potential of the cell. The absorption of water, movement of stomata and turgidity are due to osmotic potential.

Question 5.
What are the deficiency symptoms of nitrogen?
Answer:
Chlorosis, stunted growth, anthocyanin formation.

Question 6.
Explain the role of sulphur in plant biochemistry.
Answer:
Essential component of amino acids like cystine, cysteine and methionine, constituent of coenzyme A, Vitamins like biotin and thiamine, constituent of proteins and ferredoxin plants utilise sulphur as sulphate (SO4) ions.

Question 7.
Define the term Siderophores.
Answer:
Siderophores (iron carriers) are iron chelating agents produced by bacteria. They are used to chelate ferric iron (Fe3+) from environment and host.

Question 8.
List out any two iron deficiency symptoms in plants.
Answer:
Interveinal chlorosis, formation of short and slender stalk and inhibition of chlorophyll formation.

Question 9.
What is the role of Boron in plant physiology.
Answer:
Translocation of carbohydrates, uptake and utilisation of Ca++, pollen germination, nitrogen metabolism, fat metabolism, cell elongation and differentiation. It is absorbed as borate BO3-  ions.

Question 10.
Write down the deficiency symptoms of molybdenum in plants.
Answer:
Chlorosis, necrosis, delayed flowering, retarded growth and whip tail disease of cauliflower.

Question 11.
Explain briefly about aluminium toxicity on plants.
Answer:
Aluminium toxicity causes precipitation of nucleic acid, inhibition of ATPase, inhibition of cell division and binding of plasma membrane with Calmodulin.

Question 12.
Define Aeroponics.
Answer:
It is a system where roots are suspended in air and nutrients are sprayed over the roots by a motor driven rotor.

Question 13.
Define nitrogen fixation.
Answer:
The process of converting atmospheric nitrogen (N2) into ammonia is termed as nitrogen fixation. Nitrogen fixation can occur by two methods:

  1. Biological
  2. Non – Biological.

Question 14.
Mention any two ways of non – biological nitrogen fixation.
Answer:
Two ways of non – biological nitrogen fixation:

  1. Nitrogen fixation by chemical process in industry.
  2. Natural electrical discharge during lightening fixes atmospheric nitrogen.

Question 15.
Match the following.

A. Lichens (i) Anabaena Azolla
B. Anthoceros (ii) Frankia
C. Azolla (iii) Anabaena and Nostoc
D. Casuarina (iv) Nostoc

Answer:
A – (iii), B – (iv), C – (i), D – (ii).

Question 16.
Define the term Nitrate assimilation.
Answer:
The process by which nitrate is reduced to – ammonia is called nitrate assimilation and occurs during nitrogen cycle.

Question 17.
Explain.the term Transamination.
Answer:
Transfer of amino group (NH3+) from glutamic acid glutamate to keto group of keto acid. Glutamic acid is the main amino acid from which other amino acids are synthesised by transamination.

Question 18.
Explain briefly about total stem parasite.
Answer:
The leafless stem twine around the host and produce haustoria. eg: Cuscuta (Dodder), a rootless plant growing on Zizyphus, Citrus and so on.

Question 19.
Give two examples of symbiotic mode of nutrition.
Answer:
Two examples of symbiotic mode of nutrition:

  1. Lichens: It is a mutual association of Algae and Fungi. Algae prepares food and fungi absorbs water and provides thallus structure.
  2. Mycorrhizae: Fungi associated with roots of higher plants including Gymriosperms. eg: Pinus.

Question 20.
Explain briefly about insectivorous mode of nutrition.
Answer:
Plants which are growing in nitrogen deficient areas develop insectivorous habit to resolve nitrogen deficiency.

III. Answer the following (3 Marks)

Question 1.
What are the criteria required for essential minerals in plants?
Answer:
The criteria required for essential minerals in plants:

  1. Elements necessary for growth and development.
  2. They should have direct role in the metabolism of the plant.
  3. It cannot be replaced by other elements.
  4. Deficiency makes the plants impossible to complete their vegetative and reproductive phase.

Question 2.
Explain the unclassified minerals required for plants.
Answer:
Minerals like Sodium,Silicon, Cobalt and Selenium are not included in the list of essential nutrients but are required by some plants, these minerals are placed in the list of unclassified minerals. These minerals play specific roles for example, Silicon is essential for pest resistance, prevent water lodging and aids cell wall formation in Equisetaceae (Equisetum), Cyperaceae and Gramineae.

Question 3.
Distinguish between macro and micro nutrients?
Answer:
Macro nutrients:

  • Excess than 10 mmole Kg-1 in tissue concentration or 0.1 to 10 mg per gram of dry weight.
  • eg: C, H, O, N, P, K, Ca, Mg and S.

Micro nutrients:

  • Less than 10 mmole Kg-1 in tissue concentration or equal or less than 0.1 mg per gram of dry weight.
  •  eg: Fe, Mn, Cu, Mo, Zn, B, Cl and Ni.

Question 4.
Explain briefly the functions and deficiency symptoms of potassium.
Answer:
Functions: Maintains turgidity and osmotic potential of the cell, opening and closure of stomata, phloem translocation, stimulate activity of enzymes, anion and cation balance by ion – exchange. It is absorbed as K+ ions. Deficiency symptoms: Marginal chlorosis, necrosis, low cambial activity, loss of apical dominance, lodging in cereals and curled leaf margin.

Question 5.
What is meant by Chelating agents? Explain the role of EDTA as chemical chelating agent.
Answer:
Plants which are growing in alkaline soil when supplied with all nutrients including iron will show iron deficiency. To rectify this, we have to make iron into a soluble complex by adding a chelating agent like EDTA (Ethylene Diamine Tetra Acetic acid) to form Fe – EDTA.

Question 6.
Explain the term critical concentration of minerals.
Answer:
To increase the productivity and also to avoid mineral toxicity knowledge of critical concentration is essential. Mineral nutrients lesser than . critical concentration cause deficiency symptoms. Increase of mineral nutrients more than the normal concentration causes toxicity. A concentration, at which 10% of the dry weight of tissue is reduced, is considered as toxic critical concentration.

Question 7.
Describe the competitive behaviour of iron and manganese.
Answer:
Iron and Manganese exhibit competitive behaviour. Deficiency of Fe and Mn shows similar symptoms. Iron toxicity will affect absorption of manganese. The possible reason for iron toxicity is excess usage of chelated iron in addition with increased acidity of soil (pH less than 5.8) Iron and manganese toxicity will be solved by using fertilizer with balanced ratio of Fe and Mn.

Question 8.
Who are people responsible for developing hydroponics?
Answer:
Hydroponics or Soil less culture: Von Sachs developed a method of growing plants in nutrient solution. The commonly used nutrient solutions are Knop solution (1865) and Amon and Hoagland Solution (1940). Later the term Hydroponics was coined by Goerick (1940) and he also introduced commercial techniques for hydroponics. In hydroponics roots are immersed in the solution containing nutrients and air is supplied with help of tube.

Question 9.
List out the free living bacteria and fungi responsible for non-symbiotic nitrogen fixation.
Answer:
Free living bacteria and fungi also fix atmospheric nitrogen.

Aerobic Azotobacter, Beijerneckia and Derxia
Anaerobic Clostridium
Photosynthetic Chlorobium and Rhodospirillum
Chemosynthetic Disulfovibrio
Free living fungi Yeast and Pullularia
Cyanobacteria Nostoc, Anabaena and Oscillatoria.

Question 10.
Define the term Ammonification.
Answer:
Decomposition of organic nitrogen (proteins and amino acids) from dead plants and animals into ammonia is called ammonification. Organisim involved in this process are Bacillus ramosus and Bacillus vulgaris.

Question 11.
Explain briefly Catalytic amination.
Answer:
Glutamate amino acid combines with ammonia to form the amide glutamine.
Samacheer Kalvi 11th Bio Botany Solutions Chapter 12 Mineral Nutrition 8
Glutamine reacts with a ketoglutaric acid to form two molecules of glutamate.
Samacheer Kalvi 11th Bio Botany Solutions Chapter 12 Mineral Nutrition 9
(GOGAT – Glutamine – 2 – Oxoglutarate aminotransferase)

Question 12.
Compare the partial stem parasite and partial root parasite.
Answer:
The partial stem parasite and partial root parasite:

  1. Partial Stem Parasite: eg: Loranthus and Viscum (Mistletoe) Loranthus grows on fig and mango trees and absorb water and minerals from xylem.
  2. Partial root parasite: eg: Santalum album (Sandal wood tree) in its juvenile stage produces haustoria which grows on roots of many plants.

Question 13.
Explain the mode of nutrition in pitcher plant.
Answer:
Pitcher is a modified leaf and contains digestive enzymes. Rim of the pitcher is provided with nectar glands and acts as an attractive lid. When insect is trapped proteolytic enzymes will digest the insect.

Question 14.
What is meant by saprophytic mode of nutrition?
Answer:
Saprophytes derive nutrients from dead and decaying matter. Bacteria and fungus are main saprophytic organisms. Some angiosperms also follow saprophytic mode of nutrition. eg: Neottia. Roots of Neottia (Bird’s Nest Orchid) associate with mycorrhizae and absorb nutrients as a saprophyte. Monotropa (Indian Pipe) grow on humus rich soil found in thick forests. It absorbs nutrient through mycorrhizal association.

Question 15.
Describe briefly the method of nitrogen fixation in leguminous plants.
Answer:
Rhizobium bacterium is found in leguminous plants and fix atmospheric nitrogen. This kind of symbiotic association is beneficial for both the bacterium and plant. Root nodules are formed due to bacterial infection. Rhizobium enters into the-host cell and proliferates, it remains separated from the host cytoplasm by a membrane.

IV. Answer the following (5 Marks)

Question 1.
Write an essay on the functions and deficiency symptoms of macro nutrients.
Answer:
Macronutrients, their functions, their mode of absorption, deficiency symptoms and deficiency diseases are discussed here:
(i) Nitrogen (N): It is required by the plants in greatest amount. It is an essential component of proteins, nucleic acids, amino acids, vitamins, hormones, alkaloids, chlorophyll and cytochrome. It is absorbed by the plants as nitrates (NO3).

Deficiency symptoms: Chlorosis, stunted growth, anthocyanin formation.

(ii) Phosphorus (P): Constituent of cell membrane, proteins, nucleic acids, ATP, NADP, phytin and sugar phosphate. It is absorbed as H2PO4+ and HPO4 ions.

Deficiency symptoms: Stunted growth, anthocyanin formation, necrosis, inhibition of cambial activity, affect root growth and fruit ripening.

(iii) Potassium (K): Maintains turgidity and osmotic potential of the cell, opening and closure of stomata, phloem translocation, stimulate activity of enzymes, anion and cation balance by ion – exchange. It is absorbed as K+ ions.

Deficiency symptoms: Marginal chlorosis, necrosis, low cambial activity, loss of apical dominance, lodging in cereals and curled leaf margin.

(iv) Calcium (Ca): It is involved in synthesis of calcium pectate in middle lamella, mitotic spindle formation, mitotic cell division, permeability of cell membrane, lipid metabolism, activation of phospholipase, ATPase, amylase and activator of adenyl kinase. It is absorbed as Ca2+ exchangeable ions.

Deficiency symptoms: Chlorosis, necrosis, stunted growth, premature fall of leaves and flowers, inhibit seed formation, Black heart of Celery, Hooked leaf tip in Sugar beet, Musa and Tomato.

(v) Magnesium (Mg): It is a constituent of chlorophyll, activator of enzymes of carbohydrate metabolism (RUBP Carboxylase and PEP Carboxylase) and involved in the synthesis of DNA and RNA. It is essential for binding of ribosomal sub units. It is absorbed as Mg2+ ions.

Deficiency symptoms: litter veinal chlorosis, necrosis, anthocyanin (purple) formation and Sand drown of tobacco.

(vi) Sulphur (S): Essential component of amino acids like cystine, cysteine and methionine, constituent of coenzyme A, Vitamins like biotin and thiamine, constituent of proteins and ferredoxin. plants utilise sulphur as sulphate (SO4) ions.

Deficiency symptoms: Chlorosis, anthocyanin formation, stunted growth, rolling of leaf tip and reduced nodulation in legumes.

Question 2.
Describe the role of micro nutrients on plant health and function.
Answer:
Micronutrients even though required in trace amounts are essential for the metabolism of plants. They play key roles in many plants. eg: Boron is essential for translocation of sugars, molybdenum is involved in nitrogen metabolism and zinc is needed for biosynthesis of auxin. Here, we will study about the role of micro nutrients, their functions, their mode of absorption, deficiency symptoms and deficiency diseases.

(i) Iron (Fe): Iron is required lesser than macronutrient and larger than micronutrients, hence, it can be placed in any one of the groups. Iron is an essential element for the synthesis of chlorophyll and carotenoids. It is the component of cytochrome, ferredoxin, flavoprotein, formation of chlorophyll, porphyrin, activation of catalase, peroxidase enzymes. It is absorbed as ferrous (Fe2+) and ferric (Fe3+) ions. Mostly fruit trees are sensitive to iron.

Deficiency: Interveinal Chlorosis, formation of short and slender stalk and inhibition of chlorophyll formation.

(ii) Manganese (Mn): Activator of Carboxylases, oxidases, dehydrogenases and kinases, involved in splitting of water to liberate oxygen (photolysis). It is absorbed as manganous (Mn2+) ions.

Deficiency: Interveinal chlorosis, grey spot on oats leaves and poor root system.

(iii) Copper (Cu): Constituent of plastocyanin, component of phenolases, tyrosinase, enzymes involved in redox reactions, synthesis of ascorbic acid, maintains carbohydrate and nitrogen balance, part of oxidase and cytochrome oxidase. It is absorbed as cupric (Cu2+) ions,

Deficiency: Die back of citrus, Reclamation disease of cereals and legumes, chlorosis, necrosis and Exanthema in Citrus.

(iv) Zinc (Zn): Essential for the synthesis of Indole acetic acid (Auxin) activator of carboxylases, alcohol dehydrogenase, lactic dehydrogenase, glutamic acid dehydrogenase, carboxy peptidases and tryptophan synthetase. It is absorbed as Zn2+ ions.

Deficiency: Little leaf and mottle leaf due to deficiency of auxin, Inter veinal chlorosis, stunted growth, necrosis and Khaira disease of rice.

(v) Boron (B): Translocation of carbohydrates, uptake and utilisation of Ca++, pollen germination, nitrogen metabolism, fat metabolism, cell elongation and differentiation. It is absorbed as borate BO3- ions.

Deficiency: Death of root and shoot tips, premature fall of flowers and fruits, brown heart of beet root, internal cork of apple and fruit cracks.

(vi) Molybdenum (Mo): Component of nitrogenase, nitrate reductase, involved in nitrogen metabolism, and nitrogen fixation. It is absorbed as molybdate (Mo2+) ions.

Deficiency: Chlorosis, necrosis, delayed flowering, retarded growth and whip tail disease of cauliflower.

(vii) Chlorine (Cl): It is involved in Anion – Cation balance, cell division, photolysis of water. It is absorbed as Cl ions.
Deficiency: Wilting of leaf tips.

(viii) Nickel (Ni): Cofactor for enzyme urease and hydrogenase.

Deficiency: Necrosis of leaf tips.

Question 3.
Give the details of minerals and their deficiency symptoms.
Answer:
Name of the deficiency disease and symptoms:

  1. Chlorosis (Overall)
    • (a) Interveinal chlorosis
    • (b) Marginal chlorosis
  2. Necrosis (Death of the tissue)
  3. Stunted growth
  4. Anthocyanin formation
  5. Delayed flowering
  6. Die back of shoot, Reclamation disease, Exanthema in citrus (gums on bark)
  7. Hooked leaf tip
  8. Little Leaf
  9. Brown heart of turnip and Internal cork of apple
  10. Whiptail of cauliflower and cabbage
  11. Curled leaf margin

Deficiency minerals:

  1. Nitrogen, Potassium, Magnesium, Sulphur, Iron, Manganese, Zinc and Molybdenum. Magnesium, Iron, Manganese and Zinc Potassium
  2. Magnesium, Potassium, Calcium, Zinc, Molybdenum and Copper.
  3. Nitrogen, Phosphorus, Calcium, Potassium and Sulphur.
  4. Nitrogen, Phosphorus, Magnesium and Sulphur
  5. Nitrogen, Sulphur and Molybdenum
  6. Copper
  7. Calcium
  8. Zinc
  9. Boron
  10. Molybdenum
  11. Potassium

Question 4.
Give the schematic diagram of nitrogen cycle.
Answer:
The schematic diagram of nitrogen cycle:
Samacheer Kalvi 11th Bio Botany Solutions Chapter 12 Mineral Nutrition 7

Question 5.
Describe the modes of biological nitrogen fixation.
Answer:
Symbiotic bacterium like Rhizobium fixes atmospheric nitrogen. Cyanobacteria found in Lichens, Anthoceros, Azolla and coralloid roots of Cycas also fix nitrogen. Non – symbiotic (free living bacteria) like Clostridium also fix nitrogen. Symbiotic nitrogen fixation:
1. Nitrogen fixation with nodulation: Rhizobium bacterium is found in leguminous plants and fix atmospheric nitrogen. This kind of symbiotic association is beneficial for both the bacterium and plant. Root nodules are formed due to bacterial infection. Rhizobium enters into the host cell and proliferates, it remains separated from the host cytoplasm by a membrane.

2. Stages of Root nodule formation:

  • Legume plants secretes phenolics which attracts Rhizobium.
  • Rhizobium reaches the rhizosphere and enters into the root hair, infects the root hair and leads to curling of root hairs.
  • Infection thread grows inwards and separates the infected tissue from normal tissue.
  • A membrane bound bacterium is formed inside the nodule and is called bacteroid.
  • Cytokinin from bacteria and auxin from host plant promotes cell division and leads to nodule formation

3. Non – Legume: Alnus and Casuarina contain the bacterium Frankia Psychotria contains the bacterium Klebsiella.
Nitrogen fixation without nodulation. The following plants and prokaryotes are involved in nitrogen fixation:

  • Lichens – Anabaena and Nostoc
  • Anthoceros – Nostoc
  • Azolla – Anabaena azollae
  • Cycas – Anabaena and Nostoc.

Solution To Activity
Textbook Page No: 95

Question 1.
Collect leaves showing mineral deficiency. Tabulate the symptoms like Marginal Chlorosis, Interveinal Chlorosis, Necrotic leaves, Anthocyanin formation in leaf, Little leaf and Hooked leaf. (Discuss with your teacher about the deficiency of minerals)
Answer:
Symptoms:

  1. Marginal Chlorosis
  2. interveinal Chlorosis
  3. Necrotic leaves
  4. Anthocyanin formation in leaves
  5. Little leaf
  6. Hooked leaf

Minerals:

  1. Potassium (K)
  2. Magnesium (Mg)
  3. Nickel (Ni)
  4. Phosphorus (P)
  5. Zinc (Zn)
  6. Calcium (Ca)

Textbook Page No: 98

Question 1.
Preparation of Solution Culture to find out Mineral Deficiency
1. Take a glass jar or polythene bottle and cover with black paper (to prevent algal growth and roots reacting with light).
2. Add nutrient solution.
3. Fix a plant with the help of split cork.
4. Fix a tube for aeration.
5. Observe the growth by adding specific minerals.
Answer:
The deficiency of minerals like nitrogen, phosphorus, calcium, potassium and sulphur cause stunted growth in plants.

Textbook Page No: 99

Question 1.
Collect roots of legumes with root nodules.
• Take cross section of the root nodule.
• Observe under microscope. Discuss your observations with your teacher.
Answer:
Samacheer Kalvi 11th Bio Botany Solutions Chapter 12 Mineral Nutrition 1

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Samacheer Kalvi 11th Bio Botany Solutions Chapter 10 Secondary Growth

Students can Download Bio Botany Chapter 10 Secondary Growth Questions and Answers, Notes Pdf, Samacheer Kalvi 11th Bio Botany Book Solutions Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 11th Bio Botany Solutions Chapter 10 Secondary Growth

Samacheer Kalvi 11th Bio Botany Secondary Growth Text Book Back Questions and Answers

Question 1.
Consider the following statements In spring season vascular cambium:
(i) is less active
(ii) produces a large number of xylary elements
(iii) forms vessels with wide cavities of these

(a) (i) is correct but (ii) and (iii) are not correct
(b) (i) is not correct but (ii) and (iii) are correct
(c) (i) and (ii) are correct but (iii) is not correct
(d) (i) and (ii) are not correct but (iii) is correct
Answer:
(b) (i) is not correct but (ii) and (iii) are correct

Samacheer Kalvi 11th Bio Botany Solutions 10 Secondary Growth

Question 2.
Usually, the monocotyledons do not increase their girth, because:
(a) They possess actively dividing cambium
(b) They do not possess actively dividing cambium
(c) Ceases activity of cambium
(d) All are correct
Answer:
(b) They do not possess actively dividing cambium

Question 3.
In the diagram of lenticel identify the parts marked as A,B,C,D.
Samacheer Kalvi 11th Bio Botany Solutions Chapter 10 Secondary Growth 1
(a) A. Phellem, B. Complementary tissue, C. Phelloderm, D. Phellogen.
(b) A. Complementary tissue, B. Phellem, C. Phellogen, D. Phelloderm.
(c) A. Phellogen, B. Phellem, C. Pheiloderm, D. complementary tissue
(d) A. Phelloderm, B. Phellem, C. Complementary tissue, D. Phellogen
Answer:
(a) A. Phellem, B. Complementary tissue, C. Phelloderm, D. Phellogen.

Question 4.
The common bottle cork is a product of:
(a) Dermatogen
(b) Phellogen
(c) Xylem
(d) Vascular cambium
Answer:
(b) Phellogen

Question 5.
What is the fate of primary xylem in a dicot root showing extensive secondary growth?
(a) It is retained in the center of the axis
(b) It gets crushed
(c) May or may not get crushed
(d) It gets surrounded by primary phloem
Answer:
(b) It gets crushed

Samacheer Kalvi 11th Bio Botany Solutions 10 Secondary Growth

Question 6.
In a forest, if the bark of a tree is damaged by the horn of a deer, How will the plant overcome the damage?
Answer:
When the bark is damaged, the phellogem forms a complete cylinder around the stem and it gives rise to ring barks.

Question 7.
In which season the vessels of angiosperms are larger in size, why?
Answer:
In spring season the vessels are larger in size, because the cambium cells are very active during spring season.

Question 8.
Continuous state of dividing tissue is called meristem. In connection to this, what is the role of lateral meristem?
Answer:
Apical meristems produce the primary plant body. In some plants, the lateral meristem increase the girth of a plant. This type of growth is secondary because the lateral meristem are not directly produced by apical meristems. Woody plants have two types of lateral meristems: a vascular cambium that produces xylem, phloem tissues and cork cambium that produces the bark of a tree.

Question 9.
A timber merchant bought 2 logs of wood from a forest & named them A & B, The log A was 50 year old & B was 20 years old. Which log of wood will last longer for the merchant? Why?
Answer:
The wood of 50 years old will last longer than 20 years old wood, because timber from hard wood is more durable and more resistant to the attack of micro organisms and insect than the timber from sap wood.

Samacheer Kalvi 11th Bio Botany Solutions 10 Secondary Growth

Question 10.
A transverse section of the trunk of a tree shows concentric rings which are known as growth rings. How are these rings formed? What are the significance of these rings?
Answer:
The annual ring denotes the combination of early wood and late wood and the ring becomes evident to our eye due to the high density of late wood. Sometimes annual rings are called growth rings but it should be remembered all the growth rings are not annual. In some trees more than one growth ring is formed with in a year due to climatic changes. Additional growth rings are developed within a year due to adverse natural calamities like drought, frost, defoliation, flood, mechanical injury and biotic factors during the middle of a growing season, which results in the formation of more than one annual ring.

Such rings are called pseudo – or false – annual rings. Each annual ring corresponds to one year’s growth and on the basis of these rings, the age of a particular plant can easily be calculated. The determination of the age of a tree by counting the annual rings is called dendrochronology.

Samacheer Kalvi 11th Bio Botany Secondary Growth Other Important Questions & Answers

I. Choose the correct answer. (I Marks)
Question 1.
The roots and stems grow in length with the help of:
(a) cambium
(b) secondary growth
(c) apical meristem
(d) vascular parenchyma
Answer:
(c) apical meristem

Question 2.
The increase in the girth of plant is called:
(a) primary growth
(b) tertiary growth
(c) longitudinal growth
(d) secondary growth
Answer:
(d) secondary growth

Samacheer Kalvi 11th Bio Botany Solutions 10 Secondary Growth

Question 3.
The secondary vascular tissues include:
(a) secondary xylem and secondary phloem
(b) secondary xylem, cambium strip and secondary phloem
(c) secondary phloem and fascicular cambium
(d) secondary xylem and primary phloem
Answer:
(a) secondary xylem and secondary phloem

Question 4.
Choose the correct statements.
(i) A strip of vascular cambium is present between xylem and phloem of the vascular bundle.
(ii) Vascular cambium is believed originate from fusiform initials.
(iii) The vascular cambium is originated from procambium of vascular bundle
(iv) Vascular cambium is present between fusiform initials and ray initials

(a) (i) and (iv)
(b) (i) and (iii)
(c) (ii) and (iii)
(d) (ii) and (iv)
Answer:
(b) (i) and (iii)

Question 5.
Match the following:

A. Xylem (i) Treachery elements
B. Secondary xylem (ii) Water transport
C. Phloem (iii) Sieve elements
D. Secondary phloem (iv) Food transport

(a) B – (i); A – (ii); C – (iii); D – (iv)
(b) B – (ii); A – (iii); C – (i); D – (iv)
(c) A – (ii); B – (i); C – (iv); D – (iii)
(d) A – (i); B – (ii); C – (iii); D – (iv)
Answer:
(c) A – (ii); B – (i); C – (iv); D – (iii)

Samacheer Kalvi 11th Bio Botany Solutions 10 Secondary Growth

Question 6.
The axial system of the secondary xylem includes:
(a) treachery elements, sieve elements, fibers and axial parenchyma
(b) treachery elements, fibers and axial parenchyma
(c) treachery elements and fibers
(d) sieve elements and axial parenchyma
Answer:
(b) treachery elements, fibers and axial parenchyma

Question 7.
The study of wood by preparing sections for microscopic observation is termed as:
(a) histology
(b) xylotomy
(c) phoemtomy
(d) anatomy
Answer:
(b) xylotomy

Question 8.
Ray cells are present between:
(a) primary xylem and phloem
(b) primary xylem and secondary xylem
(c) secondary xylem and phloem
(d) secondary phloem and cambium
Answer:
(c) secondary xylem and phloem

Samacheer Kalvi 11th Bio Botany Solutions 10 Secondary Growth

Question 9.
The axial system Consists of vertical files of:
(a) treachery elements and sieve elements
(b) treachery elements and apical parenchyma
(c) sieve elements are fibers
(d) treachery elements, fibers and wood parenchyma
Answer:
(d) treachery elements, fibers and wood parenchyma

Question 10.
Morus rubra has:
(a) porous wood
(b) soft wood
(c) spring wood
(d) sap wood
Answer:
(a) porous wood

Question 11.
Which of the statement is not correct?
(a) In temperate regions, the cambium is very active in winter season.
(b) In temperate regions, the cambium is very active in spring season.
(c) In temperate regions, cambium is less active in winter season.
(d) In temperate regions early wood is formed in spring season.
Answer:
(a) In temperate regions, the cambium is very active in winter season.

Question 12.
Usually more distinct annual rings are formed:
(a) in tropical plants
(b) in seashore plants
(c) in temperate plants
(d) in desert plants
Answer:
(c) in temperate plants

Samacheer Kalvi 11th Bio Botany Solutions 10 Secondary Growth

Question 13.
False annual rings are formed due to:
(a) rain
(b) adverse natural calamities
(c) severe cold
(d) none of the above
Answer:
(b) adverse natural calamities

Question 14.
determination of the age of a tree by counting the annual rings is called:
(a) chronology
(b) dendrochronology
(c) palaeology
(d) histology
Answer:
(c) palaeology

Question 15.
The age of American sequoiadendron tree is about:
(a) 350 years
(b) 3,000 years
(c) 3400 years
(d) 3500 years
Answer:
(d) 3500 years

Question 16.
The wood of Acer plant has:
(a) ring porous
(b) diffuse porous
(c) central porous
(d) none of the above
Answer:
(b) diffuse porous

Samacheer Kalvi 11th Bio Botany Solutions 10 Secondary Growth

Question 17.
In fully developed tyloses:
(a) only starchy crystals are present
(b) resin and gums only are present
(c) oil and tannins are present
(d) starchy crystals, resins, gums, oils, tannins or colored substances are present
Answer:
(d) starchy crystals, resins, gums, oils, tannins or colored substances are present

Question 18.
In bombax:
(a) the sieve tubes are blocked by tylose like outgrowths
(b) the resin ducts are blocked by tylose like outgrowths
(c) the phloem tube is blocked by tylose like out growths
(d) none of the above
Answer:
(a) the sieve tubes are blocked by tylose like outgrowths

Question 19.
Which of the statement is not correct?
(a) Sap wood and heart wood can be distinguished in the secondary xylem
(b) Sap wood is paler in colour
(c) Heart wood is darker in colour
(d) The sap wood conducts minerals, while the heart wood conduct water
Answer:
(d) The sap wood conducts minerals, while the heart wood conduct water

Question 20.
Timber from heart wood is:
(a) more fragile and resistant to the attack of insects
(b) more durable and more resistant to the attack of micro organism and insects
(c) more hard and less resistant to the attack of micro organism
(d) less durable and more resistant to the attack of micro organism and insects
Answer:
(b) more durable and more resistant to the attack of micro organism and insects

Samacheer Kalvi 11th Bio Botany Solutions 10 Secondary Growth

Question 21.
The dye, haematoxylin is obtained from:
(a) the heart wood of haematoxylum campechianum
(b) the sap wood of haematoxylum campechianum
(c) cambium cells of haematoxylum campechianum
(d) the seeds of haematoxylum campechianum
Answer:
(a) the heart wood of haematoxylum campechianum

Question 22.
Canada balsam is produced from:
(a) Pisum sativum
(b) resin of Arjuna plant
(c) Abies balsamea
(d) the root of Vinca rosea
Answer:
(c) Abies balsamea

Question 23.
Some commercially important phloem or bast fibres are obtained from:
(a) banana
(b) bamboo
(c) vinca rosea
(d) cannabis sativa
Answer:
(d) cannabis sativa

Question 24.
Phellogen comprises:
(a) homogeneous sclerenchyma cells
(b)homogeneous meristamatic cells
(c) homogeneous collenchyma cells
(d) none of the above cells
Answer:
(b)homogeneous meristamatic cells

Samacheer Kalvi 11th Bio Botany Solutions 10 Secondary Growth

Question 25.
Phelloderm is otherwise called as:
(a) primary cortex
(b) cork wood
(c) secondary cortex
(d) rhytidome
Answer:
(c) secondary cortex

Question 26.
Lenticel is helpful in:
(a) transportation of food
(b) photosynthesis
(c) exchanges of gases and transpiration
(d) transportation of water
Answer:
(c) exchanges of gases and transpiration

Question 27.
The antimalarial compound quinine is, extracted from:
(a) seeds of cinchona
(b) bark of cinchona
(c) leaves of cinchona
(d) flowers of cinchona
Answer:
(b) bark of cinchona

Question 28.
Gum Arabic is obtained from:
(a) Hevea brasiliensis
(b) Acacia Senegal
(c) Pinus
(d) Dilonix regia
Answer:
(b) Acacia Senegal

Samacheer Kalvi 11th Bio Botany Solutions 10 Secondary Growth

Question 29.
Turpentine used as thinner of paints is obtained from:
(a) Acacia Senegal
(b) Vinca rosea
(c) Hevea brasiliensis
(d) Pinus
Answer:
(d) Pinus

Question 30.
Rubber is obtained from:
(a) Bombax mori
(b) Hevea brasiliensis
(c) Quercus suber
(d) Morus rubra
Answer:
(b) Hevea brasiliensis

II. Answer the following. (2 Marks)

Question 1.
Define primary growth?
Answer:
The roots and stems grow in length with the help of apical meristems. This is called primary growth or longitudinal growth.

Question 2.
Mention the two lateral meristem responsible for secondary growth.
Answer:
The secondary growth in dicots and gymnosperms is brought about by two lateral meristems.

  1. Vascular Cambium and
  2. Cork Cambium

Question 3.
What is meant by vascular cambium?
Answer:
The vascular cambium is the lateral meristem that produces the secondary vascular tissues. i.e., secondary xylem and secondary phloem.

Question 4.
Define intrafascicular or fascicular cambium?
Answer:
A strip of vascular cambium that is believed to originate from the procambium is present between xylem and phloem of the vascular bundle. This cambial strip is known as intrafascicular or fascicular cambium.

Question 5.
Define interfascicular cambium?
Answer:
In between the vascular bundles, a few parenchymatous cells of the medullary rays that are in line with the fascicular cambium become meristematic and form strips of vascular cambium. It is called interfascicular cambium.

Samacheer Kalvi 11th Bio Botany Solutions 10 Secondary Growth

Question 6.
What is vascular cambial ring?
Answer:
This interfascicular cambium joins with the intrafascicular cambium on both sides to form a continuous ring. It is called a vascular cambial ring.

Question 7.
What is meant by stratified cambium?
Answer:
If the fusiform initials are arranged in horizontal tiers, with the end of the cells of one tier appearing at approximately the same level, as seen in Tangential Longitudinal Section (TLS), it is called storied (stratified) cambium.

Question 8.
Explain non – stratified cambium.
Answer:
In plants with long fusiform initials, they strongly overlap at the ends, and this type of cambium is called non – storied (non – startified) cambium.

Samacheer Kalvi 11th Bio Botany Solutions 10 Secondary Growth

Question 9.
Give a brief note on ray initials.
Answer:
These are horizontally elongated cells. They give rise to the ray cells and form the elements of the radial system of secondary xylem and phloem.

Question 10.
How does secondary xylem or wood form?
Answer:
The secondary xylem, also called wood, is formed by a relatively complex meristem, the vascular cambium, consisting of vertically (axial) elongated fusiform initials and horizontally (radially) elongated ray initials.

Question 11.
What is meant by spring wood?
Answer:
In the spring season, cambium is very active and produces a large number of xylary elements having vessels / tracheids with wide lumen. The wood formed during this season is called spring wood or early wood.

Samacheer Kalvi 11th Bio Botany Solutions 10 Secondary Growth

Question 12.
How does the autumn wood form?
Answer:
In winter, the cambium is less active and forms fewer xylary elements that have narrow vessels /  tracheids and this wood is called autumn wood or late wood.

Question 13.
Define growth rings?
Answer:
The annual ring denotes the combination of early wood and late wood and the ring becomes evident to our eye due to the high density of late wood. Sometimes annual rings are called growth rings.

Question 14.
Define dendroclimatology?
Answer:
It is a branch of dendrochronology concerned with constructing records of past climates and climatic events by analysis of tree growth characteristics, especially growth rings.

Question 15.
Explain diffuse porous woods with an example.
Answer:
Diffuse porous woods are woods in which the vessels or pores are rather uniform in size and distribution throughout an annual ring. eg: Acer

Samacheer Kalvi 11th Bio Botany Solutions 10 Secondary Growth

Question 16.
What is meant by ring porous woods?
Answer:
The pores of the early wood are distinctly larger than those of the late wood. Thus rings of wide and narrow vessels occur.

Question 17.
Define tyloses?
Answer:
In many dicot plants, the lumen of the xylem vessels is blocked by many balloon like ingrowths from the neighbouring parenchymatous cells. These balloons like structure are called tyloses.

Question 18.
Mention two plants from which bast fibres are obtained.
Answer:
Two plants from which bast fibres are obtained:

  1. Flax – Linum ustitaissimum
  2. Hemp – Cannabis sativa

Question 19.
Define Rhytidome?
Answer:
Rhytidome is a technical term used for the outer dead bark which consists of periderm and isolated cortical or phloem tissues ? formed during successive secondary growth, eg: Quercus.

Samacheer Kalvi 11th Bio Botany Solutions 10 Secondary Growth

Question 20.
What is polyderm? Explain briefly.
Answer:
Polyderm is found in the roots and underground stems. eg: Rosaceae. It refers to a special type of protective tissues consisting of uniseriate suberized layer alternating with multiseriate nonsuberized cells in periderm.

Question 21.
Define’bark’?
Answer:
The term ‘bark’ is commonly applied to all the tissues outside the vascular cambium of stem (i.e., periderm, cortex, primary phloem and secondary phloem).

Question 22.
What are the functions of lenticel?
Answer:
Lenticel is helpful in exchange of gases and transpiration called lenticular transpiration.

Question 23.
Explain briefly phelloderm.
Answer:
It is a tissue resembling cortical living parenchyma produced centripetally (inward) from the phellogen as a part of the periderm of stems and roots in seed plants.

Question 24.
What is the function of secondary phloem?
Answer:
Secondary phloem is a living tissue that transports soluble organic compounds made during photosynthesis to various parts of plant.

Samacheer Kalvi 11th Bio Botany Solutions 10 Secondary Growth

Question 25.
what is periderm?
Answer:
Whenever stems and roots increase in thickness by secondary growth, the periderm, a protective tissue of secondary origin replaces the epidermis and Often primary cortex. The periderm consists of phellem, phellogen, and phelloderm.

III. Answer the following. (3 Marks)

Question 1.
Distinguish between primary and secondary growth.
Answer:
1. Primary growth: The plant organs originating from the apical meristems pass through a period of expansion in length and width. The roots and stems grow in length with the help of apical meristems. This is tailed primary growth or longitudinal growth.

2. Secondary growth: The gymnosperms and most angiosperms, including some monocots, show an increase in thickness of stems and roots by means of secondary growth or latitudinal growth.

Question 2.
Explain fusiform initials.
Answer:
These are vertically elongated cells. They give rise to the longitudinal or axial system of the secondary xylem (treachery elements, fibers, and axial parenchyma) and phloem (sieve elements, fibers, and axial parenchyma).

Question 3.
Explain briefly about false annual rings.
Answer:
Additional growth rings are developed within a year due to adverse natural calamities like drought, frost, defoliation, flood, mechanical injury and biotic factors during the middle of a growing season, which results in the formation of more than one annual ring. Such rings are called pseudo – or false – annual rings.

Samacheer Kalvi 11th Bio Botany Solutions 10 Secondary Growth

Question 4.
Write down the differences between spring wood and autumn wood.
Answer:
The differences between spring wood and autumn wood:

Spring wood or Early wood

Autumn wood or Late wood

1. The activity of cambium is faster. 1. Activity of cambium is slower.
2. Produces large number of xylem elements. 2. Produces fewer xylem elements.
3. Xylem vessels /  trachieds have wider lumen. 3. Xylem vessels / trachieds have narrow lumen.
4. Wood is lighter in colour and has lower density. 4. Wood is darker in colour and has a higher density.

Question 5.
How do you distinguish between sap wood and heart wood?
Answer:

Sap wood (Alburnum)

Heart wood (Duramen)

1. Living part of the wood. 1. Dead part of the wood.
2. It is situated on the outer side of wood. 2.It is situated in the certre part of wood.
3. It is less in coloured. 3. It is dark in coloured.
4. Very soft in nature. 4. Hard in nature.
Tyloses are absent.  Tyloses are present.
5. It is not durable and not resistant to microorganisms. 5. It is more durable and resists microorganisms.

Question 6.
What are fossil resins? Explain with an example.
Answer:
Plants secrete resins for their protective benefits. Amber is a fossilized tree resinespecially from the wood, which has been appreciated for its colour and natural beauty since neolithic times. Much valued from antiquity to the present as a gemstone, amber is made into a variety of decorative objects. Amber is used in jewellery. It has also been used as a healing agent in folk medicine.

Samacheer Kalvi 11th Bio Botany Solutions 10 Secondary Growth

Question 7.
Write briefly about Cork cambium.
Answer:
It is a secondary lateral meristem. It comprises homogenous meristematic cells unlike vascular cambium. It arises from epidermis, cortex, phloem or pericycle (extrastelar in origin). Its cells divide periclinally and produce radially arranged files of cells. The cells towards the outer side differentiate into phellem (cork) and those towards the inside as phelloderm (secondary cortex).

Question 8.
Explain the term lenticel.
Answer:
Lenticel is raised opening or pore on the epidermis or bark of stems and roots. It is formed during secondary growth in stems. When phellogen is more active in the region of lenticels, a mass of loosely arranged thin – walled parenchyma cells are formed. It is called complementary tissue or filling tissue. Lenticel is helpful in exchange of gases and transpiration called lenticular transpiration.

Question 9.
Mention the benefits of bark in a tree.
Answer:
Bark protects the plant from parasitic fungi and insects, prevents water loss by evaporation and guards against variations of external temperature. It is an insect repellent, decay proof, fireproof and is used in obtaining drugs or spices. The phloem cells of the bark are involved in conduction of food while secondary cortical cells involved in storage.

Samacheer Kalvi 11th Bio Botany Solutions 10 Secondary Growth

Question 10.
Distinguish between Intrafascicular Interfascicular cambium.
Answer:
Between Intrafascicular Interfascicular cambium:

Intrafascicular cambium

Interfascicular cambium

1. Present inside the vascular bundles 1. Present in between the vascular bundles.
2. Originates from the procambium. 2. Originates from the medullary rays.
3. Initially it forms a part of the primary meristem. 3. From the beginning it forms a part of the secondary meristem.

IV. Answer In detail
Question 1.
Describe the activity of vascular with the help of diagram.
Answer:
Activity of Vascular Cambium:
The vascular cambial ring, when active, cuts off new cells both towards the inner and outer side. The cells which are produced outward form secondary phloem and inward secondary xylem. At places, cambium forms some narrow horizontal bands of parenchyma which passes through secondary phloem and xylem. These are the rays. Due to the continued formation of secondary xylem and phloem through vascular cambial activity, both the primary xylem and phloem get gradually crushed.
Samacheer Kalvi 11th Bio Botany Solutions Chapter 10 Secondary Growth 6

Question 2.
Describe the formation of sap wood and heart wood with suitabie diagram.
Answer:
Sap wood and heart wood can be distinguished in the secondary xylem. In any tree the outer part of the wood, which is paler in colour, is called sap wood are alburnum. The centre part of the wood, which is darker in colour is called heart wood or duramen. The sap wood conducts water while the heart wood stops conducting water. As vessels of the heart wood are blocked by tyloses, water is not conducted through them.

Due to the presence of tyloses and their contents the heart wood becomes coloured, dead and the hardest part of the wood. From the economic point of view, generally the heartwood is more useful than the sapwood. The timber form the heartwood is more durable and more resistant to the attack of microorganisms and insects than the timber from sapwood.
Samacheer Kalvi 11th Bio Botany Solutions Chapter 10 Secondary Growth 4

Question 3.
Draw and label the transverse section of dicot stem showing the secondary growth.

Answer:
The transverse section of dicot stem showing the secondary growth:
Samacheer Kalvi 11th Bio Botany Solutions Chapter 10 Secondary Growth 5

Question 4.
Distinguish between Phellem and Phelloderm.
Answer:
Phellem (Cork):

  1. It is formed on the outer side of phellogen.
  2. Cells are compactly arranged in regular tires and rows without intercellular spaces.
  3. Protective in function.
  4. Consists of nonliving cells with suberized walls.
  5. Lenticels are present.

Phelloderm (Secondary cortex):

  1. It is formed on the inner side of phellogen.
  2. Cells are loosely arranged with intercellular spaces.
  3. As it contains chloroplast, it synthesises and stores food.
  4. Consists of living cells, parenchymatous in nature and does not have suberin.
  5. Lenticels are absent.

Question 5.
Write down the economic importance of tree bark.
Answer:
The economic importance of tree bark:
Samacheer Kalvi 11th Bio Botany Solutions Chapter 10 Secondary Growth 3

Question 5.
Draw the different stages of secondary growth in a dicot root and label the parts.
Answer:
Stages of secondary growth in a dicot root and label the parts:
Samacheer Kalvi 11th Bio Botany Solutions Chapter 10 Secondary Growth 2

Solution To Activity
Textbook Page No: 38
Question 1.
Generally monocots do not have secondary growth, but palms and bamboos have woody stems. Find the reason.
Answer:
Some of the monocots like palm and bamboos show an increase in thickness of stems by means of secondary growth or latitudinal growth.

Textbook Page No: 48
Question 2.
Be friendly with your environment (Eco friendly) Why should not we use the natural products which are made by plant fibres like rope, fancy bags, mobile pouch, mat and gunny bags etc., instead of using plastics or nylon?
Answer:
We should not use the natural products, which are made by plants fibres, because, if we use more of plant products the greedy people will exploit the plant resources for making plant products and thereby depleting the tree cover, which in turn causes reduction in rain fall.

Samacheer Kalvi 11th Bio Botany Solutions 10 Secondary Growth

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Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics

Students can Download Physics Chapter 2 Kinematics Questions and Answers, Notes Pdf, Samacheer Kalvi 11th Physics Solutions Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics

Samacheer Kalvi 11th Physics Kinematics Textual Questions Solved

Samacheer Kalvi 11th Physics Kinematics Multiple Choice Questions

Question 1.
Which one of the following Cartesian coordinate systems is not followed in physics?
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics
Answer:
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics

Question 2.
Identify the unit vector in the following:
(a) \(\hat{i}+\hat{j}\)
(b) \(\frac{\hat{i}}{\sqrt{2}}\)
(c) \(\hat{k}-\frac{\hat{j}}{\sqrt{2}}\)
(d) \(\frac{\hat{i}+\hat{j}}{\sqrt{2}}\)
Answer:
(d) \(\frac{\hat{i}+\hat{j}}{\sqrt{2}}\)

online acceleration calculator tool makes the calculation faster, and it displays the acceleration of the object in a fraction of seconds.

Question 3.
Which one of the following physical quantities cannot be represented by a scalar?
(a) Mass
(b) length
(c) momentum
(d) magnitude of acceleration
Answer:
(c) momentum

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Question 4.
Two objects of masses m1 and m2, fall from the heights h1 and h2 respectively. The ratio of the magnitude of their momenta when they hit the ground is [AIPMT 20121]
(a) \(\sqrt{\frac{h_{1}}{h_{2}}}\)
(b) \(\sqrt{\frac{m_{1} h_{1}}{m_{2} h_{2}}}\)
(c) \(\frac{m_{1}}{m_{2}} \sqrt{\frac{h_{1}}{h_{2}}}\)
(d) \(\frac{m_{1}}{m_{2}}\)
Answer:
(c) \(\frac{m_{1}}{m_{2}} \sqrt{\frac{h_{1}}{h_{2}}}\)

Question 5.
If a particle has negative velocity and negative acceleration, its speed
(a) increases
(b) decreases
(c) remains same
(d) zero
Answer:
(a) increases

Question 6.
If the velocity is\(\overrightarrow{\mathrm{v}}\) – 2\(\hat{i}\) +t2\(\hat{j}\) – 9\(\overrightarrow{\mathrm{k}}\) , then the magnitude of acceleration at t = 0.5 s is
(a) 1 m s-2
(b) 1 m
(c) zero
(d) -1 m s s-2
Answer:
(a) 1 m s-2

Question 7.
If an object is dropped from the top of a building and it reaches the ground at t = 4 s, then the height of the building is (ignoring air resistance) (g = 9.8 m s-2).
(a) 77.3 m
(b) 78.4 m
(c) 80.5 m
(d) 79.2 m
Answer:
(b) 78.4 m

Question 8.
A ball is projected vertically upwards with a velocity v. It comes back to ground in time t. Which v -1 graph shows the motion correctly?[NSEP 00 – 01]
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics
Answer:
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics

Question 9.
If one object is dropped vertically downward and another object is thrown horizontally from the same height, then the ratio of vertical distance covered by both objects at any instant is
(a) 1
(b) 2
(c) 4
(d) 0.5
Answer:
(a) 1

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Question 10.
A ball is dropped from some height towards the ground. Which one of the following represents the correct motion of the ball?
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics
Answer:
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics

Question 11.
If a particle executes uniform circular motion in the xy plane in clockwise direction, then the angular velocity is in
(a) +y direction
(b) +z direction
(c) -z direction
(d) -x direction
Answer:
(c) -z direction

Question 12.
If a particle executes uniform circular motion, choose the correct statement [NEET 2016]
(a) The velocity and speed are constant.
(b) The acceleration and speed are constant.
(c) The velocity and acceleration are constant.
(d) The speed and magnitude of acceleration are constant.
Answer:
(d) The speed and magnitude of acceleration are constant.

Question 13.
If an object is thrown vertically up with the initial speed u from the ground, then the time taken by the object to return back to ground is
(a) \(\frac{u^{2}}{2 g}\)
(b) \(\frac{u^{2}}{g}\)
(c) \(\frac{u}{2 g}\)
(d) \(\frac{2 u}{g}\)
Answer:
(d) \(\frac{2 u}{g}\)

Question 14.
Two objects are projected at angles 30° and 60° respectively with respect to the horizontal direction. The range of two objects are denoted as R30° and R60°– Choose the correct relation from the following:
(a) R30° = R60°
(b) R30° = 4R60°
(c) \(\mathrm{R}_{30^{\circ}}=\frac{\mathrm{R}_{60^{\circ}}}{2}\)
(d) R30° = 2R60°
Answer:
(a) R30° = R60°

Question 15.
An object is dropped in an unknown planet from height 50 m, it reaches the ground in 2 s. The acceleration due to gravity in this unknown planet is
(a) g = 20 m s-2
(b) g = 25 m s-2
(c) g = 15 m s-2
(d) g = 30 m s -2
Answer:
(a) g = 25 m s-2

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Samacheer Kalvi 11th Physics Kinematics Short Answer Questions

Question 1.
Explain what is meant by Cartesian coordinate system?
Answer:
At any given instant of time, the frame of reference with respect to which the position of the object is described in terms of position coordinates (x, y, z) is called Cartesian coordinate system.

Reference Angle Calculator is a free online tool that displays the reference angle for the given angle and its position.

Question 2.
Define a vector. Give examples.
Answer:
Vector is a quantity which is described by the both magnitude and direction. Geometrically a vector is directed line segment.
Example – force, velocity, displacement.

Question 3.
Define a scalar. Give examples.
Answer:
Scalar is a property which can be described only by magnitude.
Example – mass, distance, speed.

Question 4.
Write a short note on the scalar product between two vectors.
Answer:
The scalar product (or dot product) of two vectors is defined as the product of the magnitudes of both the vectors and the cosine of the angle between them. Thus if there are two vectors \(\overrightarrow{\mathrm{A}}\) and \(\overrightarrow{\mathrm{B}}\) having an angle 0 between them, then their scalar product is defined as \(\overrightarrow{\mathrm{A}}\) • \(\overrightarrow{\mathrm{B}}\) = AB cos 0. Here, AB and are magnitudes of \(\overrightarrow{\mathrm{A}}\) and \(\overrightarrow{\mathrm{B}}\).

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Question 5.
Write a short note on vector product between two vectors.
Answer:
The vector product or cross product of two vectors is defined as another vector having a magnitude equal to the product of the magnitudes of two vectors and the sine of the angle between them. The direction of the product vector is perpendicular to the plane containing the two vectors, in accordance with the right hand screw rule or right hand thumb rule. Thus, if\(\overrightarrow{\mathrm{A}}\) and \(\overrightarrow{\mathrm{B}}\) are two vectors, then their vector product is written as \(\overrightarrow{\mathrm{A}}\) × \(\overrightarrow{\mathrm{B}}\) which is a vector C defined by \(\overrightarrow{\mathrm{c}}\) = \(\overrightarrow{\mathrm{A}}\) x \(\overrightarrow{\mathrm{B}}\) = (AB sin 0) \(\hat{n}\)
The direction \(\hat{n}\) of \(\overrightarrow{\mathrm{A}}\) x \(\overrightarrow{\mathrm{B}}\) , i.e., \(\overrightarrow{\mathrm{c}}\) is perpendicular to the plane containing the vectors \(\overrightarrow{\mathrm{A}}\) and \(\overrightarrow{\mathrm{B}}\).

Question 6.
How do you deduce that two vectors are perpendicular?
Answer:
If two vectors \(\overrightarrow{\mathrm{A}}\) and \(\overrightarrow{\mathrm{B}}\) are perpendicular to each other than their scalar product \(\overrightarrow{\mathrm{A}}\) \(\overrightarrow{\mathrm{B}}\) = 0 because cos 90° = 0. Then he vectors \(\overrightarrow{\mathrm{A}}\) and \(\overrightarrow{\mathrm{B}}\) are said to be mutually orthogonal.

Question 7.
Define displacement and distance.
Answer:
Distance is the actual path length traveled by an object in the given interval of time during the motion. It is a positive scalar quantity. Displacement is the difference between the final and initial positions of the object in a given interval of time. It can also be defined as the shortest distance between these two positions of the object. It is a vector quantity.

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Question 8.
Define velocity and speed.
Answer:
Speed is defined as the ratio of total distance covered to the total time taken, it is a scalar quantity and always it is positive. Velocity is defined as the ratio of the displacement vector to the corresponding time interval. It is a vector quantity or it can also be defined as rate of change of displacement.

Question 9.
Define acceleration.
Answer:
Acceleration of a particle is defined as the rate of change of velocity or it can also be defined as the ratio of change in velocity to the given interval of time.

The Average Velocity calculator computes the velocity (V) based on the change in position (Δx) and the change in time (Δt).

Question 10.
What is the difference between velocity and average velocity.
Answer:
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics

Question 11.
Define a radian?
One radian is the angle subtended at the center of a circle by an arc that is equal in length to the radius of the circle.
1 rad = 57.295°

Question 12.
Define angular displacement and angular velocity.
Answer:
1. Angular displacement:
The angle described by the particle about the axis of rotation in a given time is called angular displacement.

2. Angular velocity:
The rate of change of angular displacement is called angular velocity.

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Question 13.
What is non uniform circular motion?
If the speed of the object in circular motion is not constant, then we have non-uniform circular motion. For example, when the bob attached to a string moves in vertical circle, the speed of the bob is not the same at all time Whenever the speed is not same in circular motion, the particle will have both centripetal and tangential acceleration.

Question 14.
Write down the kinematic equations for angular motion.
Answer:
Kinematic equations for circular motion are –

  1. \(\omega=\omega_{0}+\alpha t\)
  2. \(\theta=\omega_{0} t+\frac{1}{2} \alpha t^{2}\)
  3. \(\omega^{2}=\omega_{o}^{2}+2 \alpha \theta\)
  4. \(\theta=\frac{\left(\omega_{0}+\omega\right)}{2} t\)

Here,
ω0  = initial angular velocity
ω = final angular velocity
θ = angular displacement
α = angular acceleration
t = time.

Question 15.
Write down the expression for angle made by resultant acceleration and radius vector in the non uniform circular motion.
Answer:
The angle made by resultant acceleration and radius vector in the non uniform circular motion is –
\(\tan \theta=\frac{a_{t}}{\left(\frac{V^{2}}{r}\right)}\) or \(\theta=\tan ^{-1}\left(\frac{a_{t}}{\left(\frac{V^{2}}{r}\right)}\right)\)

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Samacheer Kalvi 11th Physics Kinematics Long Answer Questions

Question 1.
Explain in detail the triangle law of addition.
Answer:
Let us consider two vectors \(\overrightarrow{\mathrm{A}}\) and \(\overrightarrow{\mathrm{B}}\) as shown in figure. To find the resultant of the two vectors we apply the triangular.

Law of addition as follows:
present the vectors A and by the two adjacent sides of a triangle taken in the same order. Then the resultant is given by the third side of the triangle as shown in figure.
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics
To explain further, the head of the first vector \(\overrightarrow{\mathrm{A}}\) is connected to the tail of the second vect \(\overrightarrow{\mathrm{B}}\) Let O he the angle between\(\overrightarrow{\mathrm{A}}\) and \(\overrightarrow{\mathrm{B}}\). Then \(\overrightarrow{\mathrm{R}}\) is the resultant vector connecting the tail of the first vector \(\overrightarrow{\mathrm{A}}\) to the head of the second vector \(\overrightarrow{\mathrm{B}}\) The magnitude of \(\overrightarrow{\mathrm{R}}\). (resultant) given geometrically by the length of (OQ) and the direction of the resultant vector is the angle between \(\overrightarrow{\mathrm{R}}\). and \(\overrightarrow{\mathrm{A}}\). Thus we write
\(\overrightarrow{\mathrm{R}}\) = \(\overrightarrow{\mathrm{A}}\) +\(\overrightarrow{\mathrm{B}}\) \(\overrightarrow{\mathrm{OQ}}\) = \(\overrightarrow{\mathrm{OP}}\) + \(\overrightarrow{\mathrm{PQ}}\)

1. Magnitude of resultant vector:
The magnitude and angle of the resultant vector ar determined by using triangle law of vectors as follows.From figure, consider the triangle ABN, which is obtained by extending the side OA to ON. ABN is a right angled triangle.
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics
From figure, let R is the magnitude of the resultant of \(\overrightarrow{\mathrm{A}}\) and \(\overrightarrow{\mathrm{B}}\).
cos θ = \(\frac { AN}{ B }\) ∴ AN = B cos θ and sinθ = \(\frac { BN}{ B }\) ∴BN = B sinθ
For ∆ OBN, we have OB2 = ON2 + BN2
⇒ R2 = (A + B cos θ)2 + (B sinθ)2
⇒ R2 = A2 + B2 cos2θ + 2ABcosθ B2 sin2θ
⇒ R2 = A2 + B2(cos2θ + sin2θ) + 2AB cos θ
⇒ R2 = \(\sqrt{A^{2}+B^{2}+2 A B \cos \theta}\)

2. Direction of resultant vectors:
If 0 is the angle between \(\overrightarrow{\mathrm{A}}\) and \(\overrightarrow{\mathrm{B}}\) then,
\(|\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}|=\sqrt{\mathrm{A}^{2}+\mathrm{B}^{2}+2 \mathrm{AB} \cos \theta}\)
If R makes an angle α with \(\overrightarrow{\mathrm{A}}\) , then in AOBN,
tan α = \(\frac { BN}{ ON }\) = \(\frac { BN}{ OA + AN }\)
tan α = \(\frac { B sinθ }{ A + B cosθ}\) ⇒ α = \(\tan ^{-1}\left(\frac{B \sin \theta}{A+B \cos \theta}\right)\)

Question 2.
Discuss the properties of scalar and vector products.
Answer:
Properties of scalar product of two vectors are:
(1) The product quantity \(\overrightarrow{\mathrm{A}}\) . \(\overrightarrow{\mathrm{B}}\) is always a scalar. It is positive if the angle between the vectors is acute (i.e., < 90°) and negative if the angle between them is obtuse (i.e. 90°<0< 180°).

(2) The scalar product is commutative, i.e. \(\overrightarrow{\mathrm{A}}\) \(\overrightarrow{\mathrm{B}}\) ≠ \(\overrightarrow{\mathrm{B}}\). \(\overrightarrow{\mathrm{A}}\)

(3) The vectors obey distributive law i.e. \(\overrightarrow{\mathrm{A}}\)(\(\overrightarrow{\mathrm{B}}\) + \(\overrightarrow{\mathrm{C}}\)) = \(\overrightarrow{\mathrm{A}}\) . \(\overrightarrow{\mathrm{B}}\) + \(\overrightarrow{\mathrm{A}}\) .\(\overrightarrow{\mathrm{C}}\)
(4) The angle between the vectors θ = \(\cos ^{-1}\left[\frac{\overrightarrow{\mathrm{A}} \cdot \overrightarrow{\mathrm{B}}}{\mathrm{AB}}\right]\)

(5) The scalar product of two vectors will be maximum when cos θ = 1, i.e. θ = 0°, i.e., when the vectors are parallel;
\((\overrightarrow{\mathrm{A}} \cdot \overrightarrow{\mathrm{B}})_{\max }=\mathrm{AB}\)

(6) The scalar product of two vectors will be minimum, when cos θ = -1, i.e. θ = 180°.
\((\overrightarrow{\mathrm{A}} \cdot \overrightarrow{\mathrm{B}})_{\min }=-\mathrm{AB}\) when the vectors are anti-parallel.

(7) If two vectors \(\overrightarrow{\mathrm{A}}\) and \(\overrightarrow{\mathrm{B}}\) are perpendicular to each other than their scalar product \(\overrightarrow{\mathrm{A}}\) .\(\overrightarrow{\mathrm{B}}\) = 0, because cos 90° 0. Then the vectors \(\overrightarrow{\mathrm{A}}\) and \(\overrightarrow{\mathrm{B}}\) are said to be mutually orthogonal.

(8) The scalar product of a vector with itself is termed as self-dot product and is given by (\(\overrightarrow{\mathrm{A}}\))2 = \(\overrightarrow{\mathrm{A}}\) . \(\overrightarrow{\mathrm{A}}\) = AA cos 0 = A2. Here angle 0 = 0°.
The magnitude or norm of the vector \(\overrightarrow{\mathrm{A}}\) is |\(\overrightarrow{\mathrm{A}}\)| = A = \(\sqrt{\overrightarrow{\mathrm{A}} \cdot \overrightarrow{\mathrm{A}}}\).

(9) In case of a unit vector \(\hat{n}\)
\(\hat{n}\) . \(\hat{n}\) = 1 x 1 x cos 0 = 1. For example, \(\hat{i}\) – \(\hat{i}\) = \(\hat{j}\) . \(\hat{j}\) = \(\hat{k}\) . \(\hat{k}\) = 1.

(10) In the case of orthogonal unit vectors, \(\hat{i}\),\(\hat{j}\) and \(\hat{k}\),
\(\hat{i}\) . \(\hat{j}\) = \(\hat{j}\).\(\hat{k}\) = \(\hat{k}\) . \(\hat{i}\)= 1.1 cos 90° = 0

(11) In terms of components the scalar product of \(\overrightarrow{\mathrm{A}}\) and \(\overrightarrow{\mathrm{B}}\) can be written as
\(\overrightarrow{\mathrm{A}}\).\(\overrightarrow{\mathrm{B}}\) = (Ax\(\hat{i}\) + Ay\(\hat{j}\) + Az\(\hat{k}\)).(Bx\(\hat{i}\) + By\(\hat{j}\) + Bz\(\hat{k}\))
= A xBx + AyBy+ AzBz, with all other terms zero.
The magnitude of vector | \(\overrightarrow{\mathrm{A}}\) | is given by
| \(\overrightarrow{\mathrm{A}}\) | = A = \(\sqrt{\mathrm{A}_{x}^{2}+\mathrm{A}_{y}^{2}+\mathrm{A}_{z}^{2}}\)

Properties of vector product of two vectors are:
(1) The vector product of any two vectors is always another vector whose direction is perpendicular to the plane containing these two vectors, i.e., orthogonal to both the vectors \(\overrightarrow{\mathrm{A}}\) and \(\overrightarrow{\mathrm{B}}\), even though the vectors \(\overrightarrow{\mathrm{A}}\) and \(\overrightarrow{\mathrm{B}}\) may or may not be mutually orthogonal.

(2) The vector product of two vectors is not commutative, i.e., \(\overrightarrow{\mathrm{A}}\) x \(\overrightarrow{\mathrm{B}}\) ≠ \(\overrightarrow{\mathrm{B}}\) x \(\overrightarrow{\mathrm{A}}\). But,
\(\overrightarrow{\mathrm{A}}\) x \(\overrightarrow{\mathrm{B}}\)=-\(\overrightarrow{\mathrm{B}}\) x \(\overrightarrow{\mathrm{A}}\).
Here it is worthwhile to note that |\(\overrightarrow{\mathrm{A}}\) x \(\overrightarrow{\mathrm{B}}\)| =
|\(\overrightarrow{\mathrm{B}}\) x \(\overrightarrow{\mathrm{A}}\)| = AB sin 0 i.e., in the case of the product vectors \(\overrightarrow{\mathrm{B}}\)=-\(\overrightarrow{\mathrm{B}}\) and \(\overrightarrow{\mathrm{B}}\) x \(\overrightarrow{\mathrm{A}}\), the magnitudes are equal but directions are opposite to each other.

(3) The vector product of two vectors will have maximum magnitude when sin 0 = 1, i.e., 0 = 90° i.e., when the vectors \(\overrightarrow{\mathrm{A}}\) and \(\overrightarrow{\mathrm{B}}\) are orthogonal to each other.
\((\overrightarrow{\mathrm{A}} \times \overrightarrow{\mathrm{B}})_{\mathrm{max}}=\mathrm{AB} \hat{n}\) = AB \(\hat{n}\)

(4) The vector product of two non-zero vectors will be minimum when sin θ = 0, i.e θ = 0° or 180°
\((\overrightarrow{\mathrm{A}} \times \overrightarrow{\mathrm{B}})_{\min }=0\)
i. e., the vector product of two non – zero vectors vanishes, if the vectors are either parallel or anti parallel.

(5) The self – cross product, i.e., product of a vector with itself is the null vector
\(\overrightarrow{\mathrm{A}}\) x \(\overrightarrow{\mathrm{A}}\) = AA sin 0° \(\hat{n}\) = \(\overrightarrow{\mathrm{0}}\) In physics the null vector 0 is simply denoted as zero.

(6) The self – vector products of unit vectors are thus zero.
\(\hat{i}\) x \(\hat{i}\) = \(\hat{ j}\) x \(\hat{j}\) = \(\hat{k}\) x \(\hat{k}\) = 0

(7) In the case of orthogonal unit vectors, \(\hat{i}\), \(\hat{j}\). \(\hat{k}\) , in accordance with the right hand screw rule:
\(\hat{i}\) x \(\hat{j}\) = \(\hat{k}\), \(\hat{j}\) x \(\hat{k}\) = \(\hat{i}\) and \(\hat{k}\) x \(\hat{i}\) = \(\hat{j}\)
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics
Also, since the cross product is not commutative,
\(\hat{j}\) x \(\hat{i}\) = –\(\hat{k}\), \(\hat{k}\) x \(\hat{j}\) = –\(\hat{i}\) and \(\hat{i}\) x \(\hat{k}\) = \(\hat{j}\)

(8) In terms of components, the vector product of two vectors \(\overrightarrow{\mathrm{A}}\) and \(\overrightarrow{\mathrm{B}}\) is –
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics
Note that in the \(\hat{j}^{\mathrm{th}}\) component the order of multiplication is different than \(\hat{i}^{\mathrm{th}}\) and \(\hat{k}^{\mathrm{th}}\) components.

(9) If two vectors \(\overrightarrow{\mathrm{A}}\) and \(\overrightarrow{\mathrm{B}}\) form adjacent sides in a parallelogram, then the magnitude of |\(\overrightarrow{\mathrm{A}}\) x \(\overrightarrow{\mathrm{B}}\)| will give the area of the parallelogram as represented graphically in figure.
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics

(10) Since we can divide a parallelogram into two equal triangles as shown in the figure, the area of a triangle with \(\overrightarrow{\mathrm{A}}\) and \(\overrightarrow{\mathrm{B}}\) as sides is \(\frac { 1 }{ 2 }\) |\(\overrightarrow{\mathrm{A}}\) x \(\overrightarrow{\mathrm{B}}\)| . This is shown in the Figure. A number of quantities used in Physics are defined through vector products. Particularly physical quantities representing rotational effects like torque, angular momentum, are defined through vector products.
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics

Question 3.
Derive the kinematic equations of motion for constant acceleration.
Answer:
Consider an object moving in a straight line with uniform or constant acceleration ‘a’. Let u be the velocity of the object at time t = 0, and v be velocity of the body at a later time t.

Velocity – time relation:
(1) The acceleration of the body at any instant is given by the first derivative of the velocity with respect to time,
a = \(\frac {dv}{dt}\) or dv = a dt
Integrating both sides with the condition that as time changes from 0 to t, the velocity changes from u to v. For the constant acceleration,
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics

(2) The velocity of the body is given by the first derivative of the displacement with respect to time.
v = \(\frac {ds}{dt}\) or ds = vdt
and since v = u + at,
we get ds = (u+ at ) dt
Assume that initially at time t = 0, the particle started from the origin. At a later time t, the particle displacement is s. Further assuming that acceleration is time-independent, we have
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics
Velocity – displacement relation:

(3) The acceleration is given by the first derivative of velocity with respect to time.
a = \(\frac {dv}{dt}\) = \(\frac {dv}{ds}\) = \(\frac {ds}{dt}\) = \(\frac {dv}{ds}\) v [since ds/dt = v] where s is displacement traverse
This is rewritten as a = \(\frac{1}{2} \frac{d v^{2}}{d s}\) or ds = \(\frac{1}{2 a} d\left(v^{2}\right)\) Integrating the above equation, using the fact when the velocity changes from u2 to v2, displacement changes from 0 to s, we get
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics
We can also derive the displacement 5 in terms of initial velocity u and final velocity v. From equation we can
write,
at = v – u
Substitute this in equation, we get
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics

SamacheerKalvi.Guru

Question 4.
Derive the equations of motion for a particle (a) falling vertically (b) projected vertically.
Answer:
’Equations of motion for a particle falling vertically downward from certain height. Consider an object of mass m falling from a height h. Assume there is no air resistance. For convenience, let us choose the downward direction as positive y – axis as shown in the figure. The object experiences acceleration ‘g’ due to gravity which is constant near the surface of the Earth. We can use kinematic equations to explain its motion. We have The acceleration \(\overrightarrow{\mathrm{a}}\) = g \(\hat{i}\)
By comparing the components, we get,
Equations of motion for a particle thrown vertically upwards,
ax = 0, ax = 0, ay = g Let us take for simplicity, ay = a = g

Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics
If the particle is thrown with initial velocity ‘u’ downward which is in negative y – axis, then velocity and position at of the particle any time t is given by
v = u + gt
v = ut + \(\frac {1}{2}\) – gt2
The square of the speed of the particle when it is at a distance y from the hill – top, is v2 = u2 + 2 gy
Suppose the particle starts from rest.
Then u = 0
Then the velocity v, the position of the particle and v2 at any time t are given by (for a point y from the hill – top)
v = gt …………(i)
y = \(\frac {1}{2}\) – gt2 …………(ii)
v2 = 2gy …………(iii)
The time (t = T) taken by the particle to reach the ground (for which y = h), is given by using equation (ii),
h = \(\frac {1}{2}\) – gT2 …………(iv)
T = \(\sqrt{\frac{2 h}{g}}\) …………(v)
The equation (iv) implies that greater the height (h), particle takes more time (T) to reach the ground. For lesser height (h), it takes lesser time to reach the ground. The speed of the particle when it reaches the ground (y = h) can be found using equation (iii), we get,
\(v_{\text {ground }}=\sqrt{2 g h}\) …………(vi)
The above equation implies that the body falling from greater height (h) will have higher velocity when it reaches the ground. The motion of a body falling towards the Earth from a small altitude (h<<R), purely under the force of gravity is called free fall. (Here R is radius of the Earth).

case (ii):
A body thrown vertically upwards:
Consider an object of mass m thrown vertically upwards with an initial velocity u. Let us neglect the air friction. In this case we choose the vertical direction as positive y axis as shown in the figure, then the acceleration a = -g (neglect air friction) and g points towards the negative y axis. The kinematic equations for this motion are,
The velocity and position of the object at any time t are,
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics
v = u – gt ……………(vii)
s = ut – \(\frac {1}{2}\) – gt2 …………..(viii)
The velocity of the object at any position y (from the point where the object is thrown) is
v2 = u2 – 2gy …………..(ix)

Question 5.
Derive the equation of motion, range and maximum height reached by the particle thrown at an oblique angle 9 with respect to the horizontal direction.
Answer:
This projectile motion takes place when the initial velocity is not horizontal, but at some angle with the vertical, as shown in Figure.
(Oblique projectile)
Examples:

  • Water ejected out of a hose pipe held obliquely.
  • Cannon fired in a battle ground.

Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics
Consider an object thrown with initial velocity at an angle θ with the horizontal.
Then,
\(\overrightarrow{\mathrm{u}}\) = ux î + uy\(\hat{j}\) .
where ux = u cos θ is the horizontal component and uy = u sin θ the vertical component of velocity. Since the acceleration due to gravity is in the direction opposite to the direction of vertical component uy , this component will gradually reduce to zero at the maximum height of the projectile. At this maximum height, the same gravitational force will push the projectile to move downward and fall to the ground. There is no acceleration along the x direction throughout the motion. So, the horizontal component of the velocity (ux = u cos θ) remains the same till the object reaches the ground. Hence after the time t, the velocity along horizontal motion vx = ux + axt = ux = u cos θ. The horizontal distance travelled by projectile m time t is sx = \(u_{x} t+\frac{1}{2} a_{x} t^{2}\)
Here, sx = x, ux = u cos θ, ax = 0
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics
Thus, x = u cos θ or t = \(\frac {x}{u cos θ}\) ……..(i)
Next, for the vertical motion vy= uy + ayt
Here uy = u sin θ, ay = -g (acceleration due to gravity acts opposite to the motion).
Thus, vy= u sin θ – gt
The vertical distance traveled by the projectile in the same time t is
Here, sy = y, uy = u sin θ, ax = -g. Then
y = u sinθ t – \(\frac {1}{2}\) – gt2 ………..(ii)
Substitute the value of t from equation (i) in equation (ii), we have .
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics
Thus the path followed by the projectile is an inverted parabola Maximum height (hmax): The maximum vertical distance travelled by the projectile during the journey is called maximum height. This is determined as follows:
For the vertical part of the motion.
\(v_{y}^{2}=u_{y}^{2}+2 a_{y} s\)
Here, uy = u sin θ, a = -g, s = hmax, and at the maximum height vy = 0
Hence, (0)2 = u2 sin2 θ = 2 ghmax or \(h_{\max }=\frac{u^{2} \sin ^{2} \theta}{2 g}\)

Time of flight (Tf):
The total time taken by the projectile from the point of projection till it hits the horizontal plane is called time of flight. This time of flight is the time taken by the projectile to go from point O to B via point A as shown
we know that sy = y = 0 (net displacement in y-direction is zero),
uy = u sin θ, ay = -g , t = Tf Then
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics
Horizontal range (R):
The maximum horizontal distance between the point of projection and the point on the horizontal plane where the projectile hits the ground is called horizontal range (R). This is found easily since the horizontal component of initial velocity remains the same. We can write Range R = Horizontal component of velocity x time of flight = u cos θ x \(\mathrm{T}_{f}=\frac{u^{2} \sin 2 \theta}{g}\) The horizontal range directly depends on the initial speed (u) and the sine of angle of projection (θ). It inversely depends on acceleration due to gravity ‘g’.
For a given initial speed u, the maximum possible range is reached when sin 2θ is maximum, sin 2θ = 1. This implies 2θ = π/2 or θ = \(\frac {π}{4}\) This means that if the particle is projected at 45 degrees with respect to horizontal, it attains maximum range, given by.
\(\mathrm{R}_{\max }=\frac{u^{2}}{g}\) ………..(vi)

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Question 6.
Derive the expression for centripetal acceleration.
Answer:
In uniform circular motion the velocity vector turns continuously without changing its magnitude (speed), as shown in figure.
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics
Note that the length of the velocity vector is not changed during the motion, implying that the speed remains constant. Even though the velocity is tangential at every point in the circle, the acceleration is acting towards the center of the circle. This is called centripetal acceleration. It always points towards the center of the circle. This is shown in the figure.
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics
The centripetal acceleration is derived from a simple geometrical relationship between position and velocity vectors.
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics

Let the directions of position and velocity vectors shift through the same angle θ in a small interval of time ∆t, as shown in figure. For uniform circular motion, r = \(\left|\vec{r}_{1}\right|\) = \(\left|\vec{r}_{2}\right|\) and v = \(\left|\vec{v}_{1}\right|\) = \(\left|\vec{v}_{2}\right|\). If the particle moves from position vector \(\vec{r}_{1}\) to \(\vec{r}_{2}\), the displacement is given by ∆\(\overrightarrow{\mathrm{r}}\) = \(\vec{r}_{2}\) – \(\vec{r}_{1}\) and the change in velocity from \(\vec{v}_{1}\) to\(\vec{v}_{2}\) is given by ∆\(\overrightarrow{\mathrm{v}}\) = \(\vec{v}_{2}\) – \(\vec{v}_{1}\),. The magnitudes of the displacement ∆r and of ∆v satisfy the following relation. \(\frac {∆r}{r}\) = \(\frac {-∆v}{v}\) = θ Here the negative sign implies that ∆v points radially inward, towards the center of the circle.
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics
For uniform circular motion v = cor, where co is the angular velocity of the particle about center. Then the centripetal acceleration can be written as.
a = -ω2r

Question 7.
Derive the expression for total acceleration in the non uniform circular motion.
Answer:
If the speed of the object in circular motion is not constant, then we have non-uniform circular motion. For example, when the bob attached to a string moves in vertical circle, the speed of the bob is not the same at all time. Whenever the speed is not same in circular motion, the particle will have both centripetal and tangential acceleration as shown in the figure.
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics
The resultant acceleration is obtained by vector sum of centripetal and tangential acceleration Since centripetal acceleration is \(\frac{v^{2}}{r}\), the magnitude of this resultant acceleration is given by –\(\dot{a}_{\mathrm{R}}=\sqrt{a_{t}^{2}+\left(\frac{v^{2}}{r}\right)^{2}}\)
This resultant acceleration makes an angle 0 with the radius vector as shown in figure.
This angle is given by tan θ = \(\frac{a_{t}}{\left(v^{2} / r\right)}\)

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Samacheer Kalvi 11th Physics Kinematics Numerical Questions

Question 1.
The position vector of the particle has length 1 m and makes 30° with the x-axis. What are the lengths of the x and y – components of the position vector?
Answer:
Given,
Length of position vector = 1 m
Angle made with x axis = 30
Solution:
Length of X component (OB) = OA cos θ
= 1 x cos 30°
= \(\frac{\sqrt{3}}{2}\) (or) 0.87 m
Length of Y component (AB) = OA sin θ = 1 x sin 30° = \(\frac { 1 }{ 2 }\) = 0.5 m.
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics

Question 2.
A particle has its position moved from \(\vec{r}_{1}\) = 3\(\hat{i}\) + 4\(\hat{j}\) to r2 = \(\hat{i}\) + 2\(\hat{i}\). Calculate the displacement vector (∆\(\overrightarrow{\mathrm{r}}\) ) and draw the \(\vec{r}_{1}\), \(\vec{r}_{2}\) and ∆\(\overrightarrow{\mathrm{r}}\) vector in a two dimensional Cartesian coordinate system.
Answer:
Given,
Position vectors \(\vec{r}_{1}\) = 3\(\hat{i}\) + 4\(\hat{j}\)
\(\vec{r}_{1}\) = \(\hat{i}\) + 2\(\hat{j}\)
Solution:
Displacement vector:
∆r= \(\vec{r}_{2}\) – \(\vec{r}_{1}\) = (1 – 3)\(\hat{i}\) + (2 – 4) \(\hat{j}\)
∆r = -2\(\hat{i}\) -2\(\hat{j}\) = -2(\(\hat{i}\) + \(\hat{j}\))
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics

The Average Velocity calculator computes the velocity (V) based on the change in position (Δx) and the change in time (Δt).

Question 3.
Calculate the average velocity of the particle whose position vector changes from \(\vec{r}_{1}\) = 5\(\hat{i}\) + 6\(\hat{j}\) to \(\vec{r}_{2}\) = 2\(\hat{i}\) + 3 \(\hat{j}\) in a time 5 seconds.
Answer:
Given,
Position vectors of a particle
\(\vec{r}_{1}\) = 5\(\hat{i}\) + 6\(\hat{j}\),
\(\vec{r}_{2}\) = 2\(\hat{i}\) + 35\(\hat{j}\)
time(t) = 5s
Solution:
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics

Question 4.
Convert the vector \(\overrightarrow{\mathrm{r}}\) = 3\(\hat{i}\) + 2\(\hat{j}\) into a unit vector.
Answer:
Given:
Position vector\(\hat{r}\) = 3\(\hat{i}\) + 2\(\hat{j}\)
Solution:
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics

Question 5.
What are the resultants of the vector product of two given vectors given by \(\overrightarrow{\mathrm{A}}\) = 4\(\hat{i}\) – 2\(\hat{j}\) + \(\hat{k}\) and \(\overrightarrow{\mathrm{B}}\) = 5\(\hat{i}\) + 3\(\hat{j}\) – 4\(\hat{k}\) ?
Answer:
Given,
Vectors \(\overrightarrow{\mathrm{A}}\) = 4\(\hat{i}\) – 2\(\hat{j}\) + \(\hat{k}\)
\(\overrightarrow{\mathrm{B}}\) = 5\(\hat{i}\) + 3\(\hat{j}\) – 4\(\hat{k}\)
Solution:
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics

Question 6.
object at an angle such that the horizontal range is 4 times of the maximum height. What is the angle of projection of the object?
Answer:
Give,
Horizontal range = 4Hmax
Solution:
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics

Question 7.
The following graphs represent velocity – time graph. Identity what kind of motion a particle undergoes in each graph.
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics
Answer:
(a) At all the points, slope of the graph is constant.
∴ \(\overrightarrow{\mathrm{a}}\) = constant

(b) No change in magnitude of velocity with respect to time
∴ \(\overrightarrow{\mathrm{v}}\) = constant

(c) Slope of this graph is greater than graph (a) but constant
∴ \(\overrightarrow{\mathrm{a}}\) = constant but greater than the graph (a)

(d) At each point slope of the curve increases.
∴ \(\overrightarrow{\mathrm{a}}\) is a variable and object is in accelerated motion.

SamacheerKalvi.Guru

Question 8.
The following velocity – time graph represents a particle moving in the positive x-direction. Analyse its motion from 0 to 7 s. Calculate the displacement covered and distance travelled by the particle from 0 to 2 s.
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics
Answer:
As per graph,
(a) From 0 to 1.5 s the particle moving in a opposite direction.

  • From 1.5 s to 2 s the particle is moving with increasing velocity.
  • From 2 s to 5 s velocity of the particle is constant of magnitude 1 ms -1
  • From 5 s to 6 s velocity of the particle is decreasing.
  • From 6 s to 7 s the particle is at rest.

(b) Distance covered by the particle – Area covered under (v -t) graph
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics
Displacement of the particle
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics

Question 9.
A particle is projected at an angle of θ with respect to the horizontal direction. Match the following for the above motion.
(a) vx – decreases and increases
(b) vy  – remains constant
(c) Acceleration – varies
(d) Position vector – remains downward
Answer:
(a) vx = remains constant
(b) vy = decreases and increases
(c) a = remains downward
(d) r = varies

Question 10.
A water fountain on the ground sprinkles water all around it. If the speed of the water coming out of the fountain is v, calculate the total area around the fountain that gets wet.
Answer:
Given,
Speed of water = v
Solution:
Water comes from a fountain can be taken as projectile and the distance covered is maximum range of projectile i.e. θ = 45°.
Range of the particle (Rmax) = \(\frac{v^{2}}{g}\) sin 2θ = \(\frac{v^{2}}{g}\)
here, Rmax is radius of the area covered.
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics

Question 11.
The following table gives the range of a particle when thrown on different planets. All the particles are thrown at the same angle with the horizontal and with the same initial speed. Arrange the planets in ascending order according to their acceleration due to gravity, (g value).
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics
Answer:
Range = \(\frac{v^{2}}{g}\) sin 2θ ∴ g α \(\frac { 1 }{ range }\)
Ascending order of the planet with respect to their “g” is Mercury, Mars, Earth, Jupiter.

Question 12.
The resultant of two vectors A and B is perpendicular to vector A and its magnitude is equal to half of the magnitude of vector B. Then the angle between A and B is
(a) 30°
(b) 45°
(c) 150°
(d) 120°
Answer:
Given:
Resultant of \(\overrightarrow{\mathrm{A}}\) & \(\overrightarrow{\mathrm{B}}\) is perpendicular to \(\overrightarrow{\mathrm{A}}\) and magnitude of resultant (C) = \(\frac { 1 }{ 2 }\) \(\overrightarrow{\mathrm{B}}\) and α = 90°
Solution:
(i) Magnitude of resultant:
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics

(ii) direction of resultant:
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics

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Question 13.
Compare the components for the following vector equations
(a) T\(\hat{j}\) -mg\(\hat{j}\) = ma\(\hat{j}\)
(b) \(\overrightarrow{\mathrm{T}}\) + \(\overrightarrow{\mathrm{F}}\) = \(\overrightarrow{\mathrm{A}}\) + \(\overrightarrow{\mathrm{B}}\)
(c) \(\overrightarrow{\mathrm{T}}\) – \(\overrightarrow{\mathrm{F}}\) = \(\overrightarrow{\mathrm{A}}\) – \(\overrightarrow{\mathrm{B}}\)
(d) T\(\hat{j}\) + mg\(\hat{j}\)= ma\(\hat{j}\)
Answer:
Components of the vectors
(a) T – mg = ma
(b) \(\overline{\mathrm{T}}_{x}+\overline{\mathrm{F}}_{x}\) = \(\overline{\mathrm{A}}_{x}+\overline{\mathrm{B}}_{x}\) (or) \(\overline{\mathrm{T}}_{y}+\overline{\mathrm{F}}_{y}=\overline{\mathrm{A}}_{y}+\overline{\mathrm{B}}_{y}\)
(c) \(\overline{\mathrm{T}}_{x}-\overline{\mathrm{F}}_{x}=\overline{\mathrm{A}}_{x}+\overline{\mathrm{B}}_{x}\)  (or) \(\overline{\mathrm{T}}_{y}-\overline{\mathrm{F}}_{y}=\overline{\mathrm{A}}_{y}+\overline{\mathrm{B}}_{y}\)
(d) T + mg = ma

Question 14.
Calculate the area of the triangle for which two of its sides are given by the vectors A = 5\(\hat{i}\) – 3\(\hat{j}\), B = 4\(\hat{i}\) + 6\(\hat{j}\) .
Answer:
Solution:
Area of the triangle = \(\frac { 1 }{ 2 }\) |\(\overrightarrow{\mathrm{A}}\) x \(\overrightarrow{\mathrm{A}}\)|
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics

Question 15.
If Earth completes one revolution in 24 hours, what is the angular displacement made by Earth in one hour? Express your answer in both radian and degree.
Answer:
Given,
time period of earth = 24 hours
Solution:
Earth covers 360° in 24 hours
∴Angular displacement m 1 hour = \(\frac { 360° }{ 24 }\) = 15° (or) \(\frac { π }{ 12 }\)
Angular displacement in radian = \(\frac { 15° }{ 57.295° }\) = 0.262 rad

Question 16.
An object is thrown with initial speed 5 ms -1 with an angle of projection 30°. What is the height and range reached by the particle?
Answer:
Given,
Initial speed (u) = 5 ms-1
Angle of projection θ = 30°
Solution:
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics

Question 17.
A foot – ball player hits the ball with speed 20 ms-1 with angle 30° with respect to horizontal direction as shown in the figure. The goal post is at a distance of 40 m from him. Find out whether ball reaches the goal post.
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics
Answer:
Given:
Initial speed (u) = 20 ms-1
Angle of projection (θ) = 30°
The distance of the goal post = 40 m
Solution:
Range of the projectile
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics
The distance of goal post is 40 m. But the range of the ball is 35.35 m only. So ball will not reach the goal post.

Question 18.
If an object is thrown horizontally with an initial speed 10 ms -1 from the top of a building of height 100 m. What is the horizontal distance covered by the particle?
Answer:
Given,
Initial speed =10 ms-1
Height of the building (h) = 100 m
Range = ?
Solution:
Range of the object = R = \(u \sqrt{\frac{2 h}{g}}\) = 10\(\sqrt{\frac{200}{9.8}}\) = 45.1 m
R = 45 m.

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Question 19.
An object is executing uniform circular motion with an angular speed of \(\frac { π }{ 12 }\) radian per second. At t = 0 the object starts at angle θ = 0. What is the angular displacement of the particle after 4 s?
Answer:
Given:
Angular speed = \(\frac { π }{ 12 }\) rad/ sec
Solution:
Angular speed = \(\frac { Angular displacement}{ time taken }\)
Angular displacement = \(\frac { π }{ 12 }\) x 4 = \(\frac { π }{ 12 }\) = 60°

Question 20.
Consider the x-axis as representing east, the v – axis as north and z – axis as vertically upwards. Give the vector representing each of the following points.
(a) 5 m north east and 2 m up
(b) 4 m south east and 3 m up
(c) 2 m north west and 4 m up
Answer:
Given,
Solution:
(a) Length along X – axis = 5 cos 45° = \(\frac{5}{\sqrt{2}}\)m
Length along Y- axis = 5 sin 45° = \(\frac{5}{\sqrt{2}}\)m
Length along Z – Axis = 2 m
In vector rotation = \(\frac{5}{\sqrt{2}}\)\(\hat{i}\) + \(\frac{5}{\sqrt{2}}\)\(\hat{j}\) + 2\(\hat{k}\) = \(\frac{5(\hat{i}+\hat{j})}{\sqrt{2}}\) + 2\(\hat{k}\)

Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics

(b) Length along X = 4 cos 45° = \(\frac{4}{\sqrt{2}}\)m
Length along Y = 4 sin 45° = \(\frac{4}{\sqrt{2}}\)m
Length along Z-axis = 3 m
In vector rotation = \(\frac{4}{\sqrt{2}}\)\(\hat{i}\) – \(\frac{4}{\sqrt{2}}\)\(\hat{i}\) + 3k = 4(\(\hat{i}\) – \(\hat{j}\)) \(\sqrt{2}+3 \hat{k}\)

(c) Length along X = – 2 cos 45° = \(\sqrt{2}+3 \hat{k}\) = \(\frac{2}{\sqrt{2}} m=\sqrt{2} m\)
Length along Y = 2 sin 45° = \(\frac{2}{\sqrt{2}} m=\sqrt{2} m\)
length along Z = 4 m
∴ In vector rotation = \(-\sqrt{2} \hat{i}+\sqrt{2} \hat{j}+4 \hat{k}\)

Question 21.
The Moon is orbiting the Earth approximately once in 27 days, what is the angle transformed by the Moon per day?
Answer:
Given,
period of moon = 27 days
Solution:
i.e. in 27 days moon covers 360°
In one day angle traversed by moon = \(\frac { 360° }{ 2H }\) = 13.3°

Question 22.
An object of mass m has angular acceleration a = 0.2 rad s2. What is the angular displacement covered by the object after 3 second? (Assume that the object started with angle zero with zero angular velocity).
Answer:
Given,
Angular acceleration = α = 0.2 rad s-2
Time = 3s
Initial velocity = 0
Solution:
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics

Samacheer Kalvi 11th Physics Kinematics Additional Questions Solved

Samacheer Kalvi 11th Physics Kinematics Multiple Choice Questions 

Question 1.
The radius of the earth was measured by –
(a) Newton
(b) Eratosthenes
(c) Galileo
(d) Ptolemy
Answer:
(b) Eratosthenes

Question 2
The branch of mechanics which deals with the motion of objects without taking force into account is –
(a) kinetics
(b) dynamics
(c) kinematics
(d) statics
Answer:
(c) kinematics

Question 3.
If the coordinate axes (x, y, z) are drawn in anticlockwise direction then the co-ordinate system is known as –
(a) Cartesian coordinate system
(b) right handed coordinate system
(c) left handed coordinate system
(d) cylindrical coordinate system
Answer:
(b) right handed coordinate system

Question 4.
The dimension of point mass is –
(a) 0
(b) 1
(c) 2
(d) kg
Answer:
(a) 0

Question 5.
If an object is moving in a straight line then the motion is known as –
(a) linear motion
(b) circular motion
(c) curvilinear motion
(d) rotational motion
Answer:
(a) linear motion

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Question 6.
An athlete running on a straight track is an example for the whirling motion of a stone attached to’a string is a –
(a) linear motion
(b) circular motion
(c) curvilinear motion
(d) rotational motion
Answer:
(a) linear motion

Question 7.
The whirling motion of a stone attached to a string is a –
(a) linear motion
(b) circular motion
(c) curvilinear motion
(d) rotational motion
Answer:
(b) circular motion

Question 8.
Spinning of the earth about its own axis is known as –
(a) linear motion
(b) circular motion
(c) curvilinear motion
(d) rotational motion
Answer:
(d) rotational motion

Question 9.
If an object executes a to and fro motion about a fixed point, is an example for –
(a) rotational motion
(b) vibratory motion
(c) circular motion
(d) curvilinear motion
Answer:
(b) vibratory motion

Question 10.
Vibratory motion is also known as –
(a) circular motion
(b) rotational motion
(c) oscillatory motion
(d) spinning
Answer:
(c) oscillatory motion

Question 11.
The motion of satellite around the earth is an example for –
(a) circular motion
(b) rotational motion
(c) elliptical motion
(d) spinning
Answer:
(a) circular motion

Question 12.
An object falling freely under gravity close to earth is –
(a) one dimensional
(b) circular motion
(c) rotational motion
(d) spinning motion
Answer:
(a) one dimensional

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Question 13.
Motion of a coin on a carrom board is an example of –
(a) one dimensional motion
(b) two dimensional motion
(c) three dimensional motion
(d) none
Answer:
(b) two dimensional motion

Question 15.
A bird flying in the sky is an example of –
(a) one dimensional motion
(b) two dimensional motion
(c) three dimensional motion
(d) none
Answer:
(c) three dimensional motion

Question 16.
Example for scalar is –
(a) distance
(b) displacement
(c) velocity
(d) angular momentum
Answer:
(a) distance

Question 17.
Which of the following is not a scalar?
(a) Volume
(b) angular momentum
(c) Relative density
(d) time
Answer:
(b) angular momentum

Question 18.
Vector is having –
(a) only magnitude
(b) only direction
(c) bot magnitude and direction
(d) either magnitude or direction
Answer:
(c) both magnitude and direction

Question 19.
“norm” of the vector represents –
(a) only magnitude
(b) only direction
(c) both magnitude and direction
(d) either magnitude or direction
Answer:
(a) only magnitude

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Question 20.
If two vectors are having equal magnitude and same direction is known as –
(a) equal vectors
(b) col-linear vectors
(c) parallel vectors
(d) on it vector
Answer:
(a) equal vectors

Question 21.
The angle between two collinear vectors is / are –
(a) 0°
(b) 90°
(c) 180°
(d) 0° (or) 180°
Answer:
(d) 0° (or) 180°

Question 22.
The angle between parallel vectors is –
(a) 0°
(b) 90°
(c) 180°
(d) 0° (or) 180°
Answer:
(a) 0°

Question 23.
The angle between anti parallel vectors is –
(a) 0°
(b) 90°
(c) 180°
(d) 0° (or) 180°
Answer:
(c) 180°

Question 24.
Unit vector is –
(a) having magnitude one but no direction
(b) \(A \widehat{A}\)
(c) \(\frac{\widehat{A}}{A}\)
(d) |A|
Answer:
(c) \(\frac{\widehat{A}}{A}\)

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Question 25.
A unit vector is used to specify –
(a) only magnitude
(b) only direction
(c) either magnitude (or) direction
(d) absolute value
Answer:
(b) only direction

Question 26.
The angle between any two orthogonal unit vectors is –
(a) 0°
(b) 90°
(c) 180°
(d) 360°
Answer:
(b) 90°

Question 27.
If \(\hat{n}\) is a unit vector along the direction of \(\overrightarrow{\mathrm{A}}\), the \(\hat{n}\) is-
(a) \(\overrightarrow{\mathrm{A}}\) A
(b) n x A
(c) \(\overrightarrow{\mathrm{A}} / \mathrm{A}\)
(d \(\overrightarrow{\mathrm{A}}\) |A|
Answer:
(c) \(\overrightarrow{\mathrm{A}} / \mathrm{A}\)

Question 28.
The magnitude of a vector can not be-
(a) positive
(b) negative
(e) zero
(cl) 90
Answer:
(b) negative

Question 29.
If R = P + Q, then which of the following is true?
(a) P > Q
(b) Q >P
(c) P = Q
(d) R > P, Q
Answer:
(d) R > P, Q

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Question 30.
A force of 3 N and 4 N are acting perpendicular to an object, the resultant force is-
(a) 9 N
(b) 16 N
(c) 5 N
(d) 7 N
Answer:
(c) 5 N

Question 31.
Torque is a-
(a) scalar
(b) vector
(c) either scalar (or) vector
(d) none
Answer:
(6) vector

Question 32.
The resultant of \(\overrightarrow{\mathrm{A}}\) + \(\overrightarrow{\mathrm{B}}\) acts along x – axis. If A = 2\(\hat{i}\) – 3 \(\hat{j}\) + 2\(\hat{k}\) then B is-
(a) -2\(\hat{i}\) + \(\hat{j}\) + \(\hat{k}\)
(b) 3\(\hat{j}\) – 2\(\hat{k}\)
(c) -2\(\hat{i}\) -3 \(\hat{j}\)
(d) -2\(\hat{i}\) – 2\(\hat{k}\)
Answer:
(b) 3\(\hat{j}\) – 2\(\hat{k}\)

Question 33.
The angle between (\(\overrightarrow{\mathrm{A}}\) + \(\overrightarrow{\mathrm{B}}\)) and (\(\overrightarrow{\mathrm{A}}\) – \(\overrightarrow{\mathrm{B}}\)) can be –
(a) only 0°
(b) only 90°
(c) between 0° and 90°
(d) between 0° and 180°
Answer:
(d) between 0° and 180°

Question 34.
If a vector \(\overrightarrow{\mathrm{A}}\) = 3\(\hat{i}\) + 2\(\hat{j}\) then what is 4 A-
(a) 12\(\hat{i}\) + 8\(\hat{j}\)
(b) 0.75\(\hat{i}\) + 0.5\(\hat{j}\)
(c) 3\(\hat{i}\) + 2\(\hat{j}\)
(d) 7\(\hat{i}\) + 6\(\hat{j}\)
Answer:
(a) 12\(\hat{i}\) + 8\(\hat{j}\)

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Question 35.
If P = mV then the direction of P along-
(a) m
(b) v
(c) both (a) and (b)
(d) neither m nor v
Answer:
(b) v

Question 36.
The scalar product \(\overrightarrow{\mathrm{A}}\). \(\overrightarrow{\mathrm{B}}\) is equal to-
(a) \(\overrightarrow{\mathrm{A}}\) + \(\overrightarrow{\mathrm{B}}\)
(b) AB sin θ
(c) AB cos θ
(d) \(\overrightarrow{\mathrm{A}}\) + \(\overrightarrow{\mathrm{B}}\)
Answer:
(c) AB cos θ

Question 37.
The scalar product \(\overrightarrow{\mathrm{A}}\).\(\overrightarrow{\mathrm{B}}\)is equal to-
(a) \(\overrightarrow{\mathrm{A}}\) +\(\overrightarrow{\mathrm{B}}\)
(b) \(\overrightarrow{\mathrm{A}}\). \(\overrightarrow{\mathrm{B}}\)
(c) AB sin θ
(d) (\(\overrightarrow{\mathrm{A}}\) x \(\overrightarrow{\mathrm{B}}\)
Answer:
(b) \(\overrightarrow{\mathrm{A}}\). \(\overrightarrow{\mathrm{B}}\)

Question 38.
The scalar product of two vectors will be maximum when θ is equal to –
(a) 0°
(b) 90°
(c) 180°
(d) 270°
Answer:
(a) 0°

Question 39.
The scalar product of two vectors will be minimum. When θ is equal to –
(a) 0°
(b) 45°
(c) 180°
(d) 60°
Answer:
(c) 180°

Question 40.
The vectors A and B to be mutually orthogonal when –
(a) \(\overrightarrow{\mathrm{A}}\) + \(\overrightarrow{\mathrm{B}}\) = 0
(b) \(\overrightarrow{\mathrm{A}}\) –\(\overrightarrow{\mathrm{B}}\) = 0
(c) \(\overrightarrow{\mathrm{A}}\).\(\overrightarrow{\mathrm{B}}\) = 0
(d) \(\overrightarrow{\mathrm{A}}\) x \(\overrightarrow{\mathrm{B}}\) = 0
Answer:
(c) \(\overrightarrow{\mathrm{A}}\).\(\overrightarrow{\mathrm{B}}\) = 0

Question 41.
The magnitude of the vector is –
(a) A2
(b) \(\sqrt{\mathrm{A}^{2}}\)
(c) \(\sqrt{\mathrm{A}}\)
(d) \(\sqrt[3]{\mathrm{A}}\)
Answer:
(b) \(\sqrt{\mathrm{A}^{2}}\)

Question 42.
\(\hat{i}\) .\(\hat{j}\) is –
(a) 0
(b) I
(c) ∞
(d) none
Answer:
(a) 0

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Question 43.
If \(\overrightarrow{\mathrm{A}}\) and \(\overrightarrow{\mathrm{B}}\) are two vectors, which are acting along x, y respectively, then \(\overrightarrow{\mathrm{A}}\) and \(\overrightarrow{\mathrm{B}}\) lies along –
(a) x
(b) y
(c) z
(d) none
Answer:
(c) z

Question 44.
The direction of \(\overrightarrow{\mathrm{A}}\) x \(\overrightarrow{\mathrm{B}}\) is given by-
(a) right hand screw rule
(b) right hand thumb rule
(c) both (a) and (b)
(d) neither (a) and (b)
Answer:
(c) both (a) and (b)

Question 45.
\(\overrightarrow{\mathrm{A}}\) x \(\overrightarrow{\mathrm{B}}\) is –
(a) AB cos θ
(b) AB sin θ
(c) AB tan θ
(d) AB sec θ
Answer:
(b) AB sin θ

Question 46.
\(\overrightarrow{\mathrm{A}}\) x \(\overrightarrow{\mathrm{B}}\) isequal to –
(a) \(\overrightarrow{\mathrm{B}}\) x \(\overrightarrow{\mathrm{A}}\)
(b) \(\overrightarrow{\mathrm{A}}\) + \(\overrightarrow{\mathrm{B}}\)
(c) –\(\overrightarrow{\mathrm{B}}\) x \(\overrightarrow{\mathrm{A}}\)
(d) \(\overrightarrow{\mathrm{A}}\) – \(\overrightarrow{\mathrm{B}}\)
Answer:
(c) –\(\overrightarrow{\mathrm{B}}\) x \(\overrightarrow{\mathrm{A}}\)

Question 47.
The vector product of any two vectors gives a –
(a) vector
(b) scalar
(e) tensor
(d) col-linear
Answer:
(a) vector

Question 48.
|\(\overrightarrow{\mathrm{A}}\) x \(\overrightarrow{\mathrm{B}}\)| is equal to –
(a) -|\(\overrightarrow{\mathrm{A}}\) x \(\overrightarrow{\mathrm{B}}\)|
(b) |\(\overrightarrow{\mathrm{B}}\) x \(\overrightarrow{\mathrm{A}}\)|
(c) -|\(\overrightarrow{\mathrm{B}}\) x \(\overrightarrow{\mathrm{A}}\)|
(d) \( \frac{\overline{\mathrm{A}} \times \overline{\mathrm{B}}}{|\overline{\mathrm{A}} \times \overline{\mathrm{B}}|}\)
Answer:
(b) |\(\overrightarrow{\mathrm{B}}\) x \(\overrightarrow{\mathrm{A}}\)|

Question 49.
The vector product of two vectors will have maximum magnitude when θ is equal to –
(a) 0°
(b) 90°
(c) 180°
(d) 360°
Answer:
(b) 90°

Question 50.
The vector product of two non-zero vectors will be minimum when O is equal to –
(a) 0°
(b) 180°
(e) both (a) and (b)
(d) neither (a) nor (b)
Answer:
(e) both (a) and (b)

Question 51.
The product of a vector with itself is equal to –
(a) 0
(b) 1
(c) ∞
(d) A2
Answer:
(a) 0

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Question 52.
\(\hat{i}\) x \(\hat{i}\) is –
(a) 0
(b) 1
(c) ∞
(d) \(\hat{j}\)
Answer:
(a) 0

Question 53.
\(\hat{i}\) x \(\hat{j}\) is –
(a) \(\hat{i}\)
(b) \(\hat{j}\)
(c) \(\hat{k}\)
(d) \(\overrightarrow{\mathrm{z}}\)
Answer:
(c) \(\hat{k}\)

Question 54.
\(\hat{j}\) x \(\hat{i}\) is –
(a) –\(\hat{i}\)
(b) –\(\hat{j}\)
(c) –\(\hat{k}\)
(d) \(\overrightarrow{\mathrm{z}}\)
Answer:
(c) –\(\hat{k}\)

Question 55.
If two vectors \(\overrightarrow{\mathrm{A}}\) and \(\overrightarrow{\mathrm{B}}\) form adjacent sides of parallelogram, then the magnitude of |\(\overrightarrow{\mathrm{A}}\) x \(\overrightarrow{\mathrm{B}}\)| will give of parallelogram –
(a) length
(b) area
(c) volume
(d) diagonal
Answer:
(b) area

Question 56.
If \(\overrightarrow{\mathrm{P}}\) – \(\overrightarrow{\mathrm{Q}}\) then which of the following is incorrect. –
(a) \(\hat{P}\) = \(\hat{Q}\)
(b) |\(\hat{P}\)| = |\(\hat{Q}\)|
(c) P\(\hat{Q}\) = Q\(\hat{A}\)
(d) \(\hat{P}\) \(\hat{Q}\) = PQ
Answer:
(d) \(\hat{P}\) \(\hat{Q}\) = PQ

Question 57.
The momentum of a particle is \(\overrightarrow{\mathrm{P}}\) = cos θ \(\hat{i}\) + sin θ \(\hat{j}\) . The angle between momentum and the force acting on a body is –
(a) 0°
(b) 45°
(c) 90°
(d) 180°
Answer:
(c) 90°

Question 58.
A and B are two vectors, if A and B are perpendicular to each other then –
(a) \(\overrightarrow{\mathrm{A}}\) x \(\overrightarrow{\mathrm{B}}\) = 0
(b) \(\overrightarrow{\mathrm{A}}\) x \(\overrightarrow{\mathrm{B}}\) = l
(c) \(\overrightarrow{\mathrm{A}}\) \(\overrightarrow{\mathrm{B}}\) = 0
(d) \(\overrightarrow{\mathrm{A}}\) \(\overrightarrow{\mathrm{B}}\) = \(\overrightarrow{\mathrm{A}}\)\(\overrightarrow{\mathrm{B}}\)
Answer:
(c) \(\overrightarrow{\mathrm{A}}\) \(\overrightarrow{\mathrm{B}}\) = 0

Question 59.
The angle between two vectors -3\(\hat{i}\) + 6\(\hat{k}\) and 2\(\hat{i}\) + 3\(\hat{j}\) + \(\hat{k}\) is –
(a) 0°
(b) 45°
(c) 60°
(d) 90°
Answer:
(d) 90°

Question 60.
The radius vector is 2\(\hat{i}\) + \(\hat{j}\) + \(\hat{k}\) while linear momentum is 2\(\hat{i}\) + 3\(\hat{j}\) + \(\hat{k}\) Then the angular momentum is
(a) -2\(\hat{i}\) + 4\(\hat{k}\)
(b) 4\(\hat{i}\) – 8\(\hat{k}\)
(c) 2\(\hat{k}\) – 4\(\hat{j}\) + 2\(\hat{k}\)
(d) 4\(\hat{i}\) – 8\(\hat{j}\)
Answer:
(a) -2\(\hat{i}\) + 4\(\hat{k}\)

Question 61.
Which of the following cannot be a resultant of two vectors of magnitude 3 and 6?
(a) 3
(b) 6
(c) 10
(d) 7
Answer:
(c) 10

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Question 62.
Twelve forces each of magnitude 10 N acting on a body at an angle of 30° with other forces then their resultant is-
(a) 10 N
(b)120 N
(c) \(\frac{10}{\sqrt{3}}\)
(d) zero

Question 63.
Two forces are in the ratio of 3 : 4. The maximum and minimum of their resultants are in the ratio is –
(a) 4 : 3
(b) 3 : 4
(c) 7 : 1
(d) 1 : 7
Answer:
(c) 7 : 1

Question 64.
If | \(\overrightarrow{\mathrm{P}}\) + \(\overrightarrow{\mathrm{Q}}\) | = |\(\overrightarrow{\mathrm{P}}\) | + |\(\overrightarrow{\mathrm{Q}}\)|. The angle between the vectors \(\overrightarrow{\mathrm{P}}\) and \(\overrightarrow{\mathrm{Q}}\) is –
(a) 0°
(b) 180°
(c) 60°
(d) 90°
Answer:
(a) 0°
|\(\overrightarrow{\mathrm{P}}\) + \(\overrightarrow{\mathrm{Q}}\) | = |\(\overrightarrow{\mathrm{P}}\) | + |\(\overrightarrow{\mathrm{Q}}\)|
Square on both sides and the resultant becomes
P2 + Q2 + 2PQ cos θ = P2 + Q2 + 2PQ cos θ = 1
θ = 0

Question 65.
If |\(\overrightarrow{\mathrm{P}}\) + \(\overrightarrow{\mathrm{Q}}\) = |\(\overrightarrow{\mathrm{P}}\) | — |\(\overrightarrow{\mathrm{P}}\)|, then the angle between the vectors \(\overrightarrow{\mathrm{P}}\) and \(\overrightarrow{\mathrm{Q}}\)
(a) 0°
(b) 90°
(c) 180°
(d) 360°
Answer:
(c) |\(\overrightarrow{\mathrm{P}}\) + \(\overrightarrow{\mathrm{Q}}\)| = |\(\overrightarrow{\mathrm{P}}\) | |\(\overrightarrow{\mathrm{P}}\)| ‘
Square on both side, and the resultant becomes
P2 + Q2 + 2PQ cos θ = P2 + Q2 – 2PQ .
cos θ = -1
θ = 180°

Question 66.
If |\(\overrightarrow{\mathrm{P}}\) x \(\overrightarrow{\mathrm{Q}}\)| = |\(\overrightarrow{\mathrm{P}}\) . \(\overrightarrow{\mathrm{Q}}\)| then angle between \(\overrightarrow{\mathrm{P}}\) and \(\overrightarrow{\mathrm{Q}}\) then angle between P and Q will be –
(a) 0°
(b) 30°
(c) 45°
(d) 60°
Answer:
(c) |\(\overrightarrow{\mathrm{P}}\) x \(\overrightarrow{\mathrm{Q}}\)| = |\(\overrightarrow{\mathrm{P}}\) . \(\overrightarrow{\mathrm{Q}}\)| Expand the terms
PQ sinθ = PQ cos θ
tan θ = 1
θ = 45°

Question 67.
If | \(\overrightarrow{\mathrm{P}}\) + \(\overrightarrow{\mathrm{Q}}\) | = |\(\overrightarrow{\mathrm{P}}\) | |\(\overrightarrow{\mathrm{Q}}\)|, then angle between \(\overrightarrow{\mathrm{P}}\) and \(\overrightarrow{\mathrm{Q}}\) will be –
(a) 0°
(b) 45°
(c) 90°
(d) 180°
Answer:
(c) | \(\overrightarrow{\mathrm{P}}\) + \(\overrightarrow{\mathrm{Q}}\) | = |\(\overrightarrow{\mathrm{P}}\)| |\(\overrightarrow{\mathrm{Q}}\) |
Square on both side, and the resultants become,
P2 + Q2 + 2PQ cos 0 = P2 + Q2 – 2PQ cos θ 4PQ cos θ = 0
θ = 90°

Question 68.
If A and B are the sides of triangle, then area of triangle –
(a) \(\frac{1}{2}|\overrightarrow{\mathrm{A}} \cdot \overrightarrow{\mathrm{B}}|\)
(b) \(\frac{1}{2}|\overrightarrow{\mathrm{A}} \times \overrightarrow{\mathrm{B}}|\)
(c) AB sin θ
(d) AB cos θ
Answer:
(b) \(\frac{1}{2}|\overrightarrow{\mathrm{A}} \times \overrightarrow{\mathrm{B}}|\)

Question 69.
A particle moves in a circular path of radius 2 cm. If a particle completes 3 rounds, then the distance and displacement of the particle are –
(a) 0 and 37.7
(b) 37.7 and 0
(c) 0 and 0
(d) 37.7 and 37.7
Answer:
(b) Radius = 2 cm
Circumference of the circle = 2nr = 4n cm
Distance covered in 3 rounds = 127r cm = 37.7 cm
Initial and final positions are same
∴ Displacement = 0

Question 70.
If rx and r2 are position vectors, then the displacement vector is –
(a) \(\vec{r}_{1} \times \vec{r}_{2}\)
(b) \(\vec{r}_{1} \cdot \vec{r}_{2} \)
(c) \(\vec{r}_{1}+\vec{r}_{2}\)
(d) \(\vec{r}_{2}+\vec{r}_{1} \)
Answer:
(d) \(\vec{r}_{2}+\vec{r}_{1} \)

Question 71.
The ratio of the displacement vector to the corresponding time interval is –
(a) average speed
(b) average velocity
(c) instantaneous speed
(d) instantaneous velocity
Answer:
(b) average velocity

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Question 72.
The ratio of total path length travelled by the particle in a time interval –
(a) average speed
(b) average velocity
(c) instantaneous speed
(d) instantaneous velocity
Answer:
(a) average speed

Question 73.
The product of mass and velocity of a particle is –
(a) acceleration
(b) force
(c) torque
(d) momentum
Answer:
(d) momentum

Question 74.
The area under the force, displacement curve is –
(a) potential energy
(b) work done.
(c) impulse
(d) acceleration
Answer:
(b) work done

Question 75.
The area under the force, time graph is –
(a) momentum
(b) force
(c) work done
(d) impulse
Answer:
(d) impulse

Question 76.
The unit of momentum is –
(a) kg ms-1
(b) kg ms-2
(c) kg m2s-1
(d) kg-1 m2 s-1
Answer:
(b) kg ms-2

Question 77.
The slope of the position – time graph will give –
(a) displacement
(b) velocity
(c) acceleration
(d) force
Answer:
(d) force

Question 78.
The area under velocity-time graph gives-
(a) positive
(b) negative
(c) either positive (or) negative
(d) zero
Answer:
(c) either positive (or) negative

Question 79.
The magnitude of distance is always-
(a) positive
(b) negative
(c) either positive (or) negative
(d) zero
Answer:
(a) positive

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Question 80.
If two objects A and B are moving along a straight line in the same direction with the velocities vA and vB respectively, then the relative velocity is-
(a) vA + vB
(b) vA – vB
(c) vA vB
(d) vA / vB
Answer:
(b) VA – VB

Question 81.
If two objects A and B are moving along a straight line in the opposite direction with the velocities VA and VB respectively, then relative velocity is-
(a) VA + VB
(b) VA – VB
(c) VA . VB
(d) VA / VB
Answer:
(a) VA + VB

Question 82.
If two objects moving with a velocities of VA and VB at an angle of 0 between them, the relative velocity is –
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics
Answer:
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics

Question 83.
A person moving horizontally with velocity \(\overrightarrow{\mathrm{V}_{m}}\) The relative velocity of rain with respect to the person is –
(a) \(\mathrm{V}_{\mathrm{R}}+\mathrm{V}_{\mathrm{m}}\)
(b) \(\sqrt{\mathrm{V}_{\mathrm{R}}+\mathrm{V}_{m}}\)
(c) \(\mathrm{V}_{\mathrm{R}}-\mathrm{V}_{m}\)
(d) \(\sqrt{\mathrm{v}_{\mathrm{R}}^{2}+\mathrm{V}_{m}^{2}}\)
Answer:
(d) \(\sqrt{\mathrm{v}_{\mathrm{R}}^{2}+\mathrm{V}_{m}^{2}}\)

Question 84.
A person moving horizontally with velocity \(\overrightarrow{\mathrm{V}_{m}}\) . Rain falls vertically with velocity \(\overrightarrow{\mathrm{V}_{R}}\) To save himself from the rain, he should hold an umbrella with vertical at an angle of –
(a) \(\tan ^{-1}\left(\frac{V_{R}}{V_{m}}\right)\)
(b) \(\tan ^{-1}\left(\frac{V_{m}}{V_{R}}\right)\)
(c) \(\tan \theta=\mathrm{V}_{m}+\mathrm{V}_{\mathrm{R}}\)
(d) \(\tan ^{-1}\left(\mathrm{V}_{\mathrm{R}}+\mathrm{V}_{m} / \mathrm{V}_{\mathrm{R}}-\mathrm{V}_{m}\right)\)
Answer:
(b) \(\tan ^{-1}\left(\frac{V_{m}}{V_{R}}\right)\)

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Question 85.
A car starting from rest, accelerates at a constant rate x for sometime after which it decelerates at a constant rate v to come to rest. If the total time elapsed is t, the maximum velocity attained by the car is given by –
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics
Answer:
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics

Question 86.
A car covers half of its journey with a speed of 10 ms-1 and the other half by 20 ms-1. The average speed of car during the total journey is –
(a) 70 ms-1
(b) 15 ms-1
(c) 13.33 ms-1
(d) 7.5 ms-1
Answer:
(c) Let x is the total distance
Time to cover 1st half = \(\frac{x / 2}{10}\)
Time to cover 2nd half = \(\frac{x / 2}{20}\)
Average speed =
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics

Question 87.
A swimmer can swim in still water at of 10 ms-1 While crossing a river his average speed is 6 ms-1. If he crosses the river in the shortest possible time, what is the speed of flow of water?
(a) 16 ms-1
(b) 4 ms-1
(c) 60 ms-1
(d) 8 ms-1
Answer:
(d) The resultant velocity of swimmer must be perpendicular to speed of water to cross the river in a shortest time
∴ \(v_{s}^{2}=v^{2}+v_{w}^{2}\)
\(v_{w}^{2}=v_{s}^{2}-v^{2}\) = 100 – 36 = 64
∴ V = 8 m/s-1

Question 88.
A 100 m long train is traveling from North to South at a speed of 30 ms-1. A bird is flying from South to North at a speed of 10-1. How long will the bird take to, cross the train?
(a) 3 s
(b) 2.5 s
(c) 10 s
(d) 5 s
Answer:
(b) Length of train = 100 m
Relative velocity = 30 + 10 = 40 ms-1
Time taken to cross the train (t) = \(\frac {distance}{ R.velocity }\) = \(\frac { 100 }{ 40 }\) = 2.5 s

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Question 89.
The first derivative of position vector with respect to time is –
(a) velocity
(b) acceleration
(c) force
(d) displacement
Answer:
(a) velocity

Question 90.
The second derivative of position vector with respect to time is –
(a) velocity
(b) acceleration
(c) force
(d) displacement
Answer:
(b) acceleration

Question 91.
The slope of displacement-time graph gives –
(a) velocity
(b) acceleration
(c) force
(d) displacement
Answer:
(a) velocity

Question 92.
The slope of velocity-time graph gives –
(a) velocity
(b) acceleration
(c) force
(d) displacement
Answer:
(b) acceleration

Question 93.
The position vector of a particle is \(\vec{r}\) = 4t2\(\hat{i}\) + 2t\(\hat{j}\) + 3t\(\hat{k}\) The acceleration of a particle is having only –
(a) X – component
(b) Y – component
(c) Z – component
(d) X – Y component
Answer:
(a) X – component
4t2\(\hat{i}\) + 2t\(\hat{j}\) + 3t\(\hat{k}\)
\(\vec{v}\) = \(\frac{d \vec{r}}{dt}\) = 8t\(\hat{i}\) + 2\(\hat{j}\)
a = \(\frac{d^{2} r}{d t^{2}}\) = 8\(\hat{i}\) a is having only X-component.

Question 94.
The position vector of a particle is \(\vec{r}\) = 4t2\(\hat{i}\) + 2t\(\hat{j}\) + 3t\(\hat{k}\). The speed of the particle at t = 5 s is –
(a) 42 ms-1
(b) 3s
(c) 3 ms-1
(d) 40 ms-1
Answer:
(a) 42 ms-1
\(\vec{r}\) = 4t2\(\hat{i}\) + 2t\(\hat{j}\) + 3t\(\hat{k}\)
Speed v = — = \(\frac{d \vec{r}}{dt}\) = 8t\(\hat{i}\) + 2\(\hat{j}\)
at t = 5 s v = 40 + 2 = 42

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Question 95.
An object is moving in a straight line with uniform acceleration a, the velocity-time relation is –
(a) u = v + at
(b) v = u + at
(c) v2 = u2 + a2t2
(d) v2 – u2 = at
Answer:
(b) v = u + at

Question 96.
An object is moving in a straight line with uniform acceleration, the displacement-time relation is –
(a) S = \(u t^{2}+\frac{1}{2} a t^{2}\)
(b) S = \(u t-\frac{1}{2} a t^{2}\)
(c) S = \(u t+\frac{1}{2} a t^{2}\)
(d) S = \(u t-a t^{2}\)
Answer:
(c) S = \(u t+\frac{1}{2} a t^{2}\)

Question 97.
An object is moving in a straight line with uniform acceleration, the velocity-displacement reflation is –
(a) V = u + 2as
(b) S = ut + -at
(c) V2 = u2 – 2as
(d) V2 = u2 + 2as
Answer:
(d) V2 = u2 + 2as

Question 98.
For free-falling body, its initial velocity is –
(a) 0
(b) 1
(c) ∞
(d) none
Answer:
(a) 0

Question 99.
An object falls from a height h (h<<R), the speed of the object when it reaches the ground is –
(a) \(\frac{1}{2} g t^{2}\)
(b) \(\sqrt{g t}\)
(c) gh
(d) \(\sqrt{2 g h}\)
Answer:
(d) \(\sqrt{2 g h}\)

Question 100.
An object falls from a height h (h<< R) the time taken by an object to reaches the ground is –
(a) \(\frac{1}{2} g t^{2}\)
(b) \(\sqrt{2 g h}\)
(c) \(\sqrt{\frac{2 h}{g}}\)
(d) \(\sqrt{\frac{2 g}{h}}\)
Answer:
(d) \(\sqrt{\frac{2 g}{h}}\)

Question 101.
In the absence of air resistance, horizontal velocity of the projectile is –
(a) always negative
(b) equal to ‘g’
(c) directly proportional to g
(d) a constant
Answer:
(d) a constant

Question 102.
In the horizontal projection, the range of the projectile is –
(a) \(\sqrt{\frac{2 h}{g}}\)
(b) \(u \sqrt{\frac{h}{g}}\)
(c) \(u \sqrt{\frac{2 h}{g}}\)
(d) \(u \sqrt{\frac{g}{2 h}}\)
Answer:
(c) \(u \sqrt{\frac{2 h}{g}}\)

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Question 103.
In oblique projection, maximum height attained by the projectile is –
(a) \(\frac { t }{ u cos θ }\)
(b) \(\frac { u cos θ }{ 2g }\)
(c) \(\frac { 2g }{ u cos θ }\)
(d) \(\frac{u^{2} \sin ^{2} \theta}{2 g}\)
Answer:
(d) \(\frac{u^{2} \sin ^{2} \theta}{2 g}\)

Question 104.
In oblique projection time of flight of a projectile is –
(a) \(\frac{u^{2} \sin ^{2} \theta}{2 g}\)
(b) \(\frac { 2u cos θ }{ g }\)
(c) \(\frac{u^{2} \sin 2 \theta}{g}\)
(d) \(\frac{u^{2}}{g}\)
Answer:
(b) \(\frac { 2u cos θ }{ g }\)

Question 105.
In oblique projection horizontal range of the projectile is –
(a) \(\frac{u^{2} \sin ^{2} \theta}{2 g}\)
(b) \(\frac { 2u cos θ }{ g }\)
(c) \(\frac{u^{2} \sin 2 \theta}{g}\)
(d) \(\frac{u^{2}}{g}\)
Answer:
(a) \(\frac{u^{2} \sin ^{2} \theta}{2 g}\)

Question 106.
In oblique projection, maximum horizontal range of the projectile is –
(a) \(\frac{u^{2} \sin ^{2} \theta}{2 g}\)
(b) \(\frac { 2u cos θ }{ g }\)
(c) \(\frac{u^{2} \sin 2 \theta}{g}\)
(d) \(\frac{u^{2}}{g}\)
Answer:
(d) \(\frac{u^{2}}{g}\)

Question 107.
One radian is equal to –
(a) \(\frac {π}{ 180 }\) degree
(b) 60°
(c) 57.295°
(d) 53.925°
Answer:
(c) 57.295°

Question 108.
In relation between linear and angular velocity is –
(a) ω = vr
(b) ω = \(\frac {v }{ r }\)
(c) ω = \(\frac { r}{ v }\)
(d) ω = \(\frac { r }{ ω }\)
Answer:
(b) ω = \(\frac {v }{ r }\)

Question 109.
Centripetal acceleration is given by –
(a) \(\frac{v^{2}}{r}\)
(b) \(-\frac{v^{2}}{r}\)
(c) \(\frac{r}{v^{2}}\)
(d) \(-\frac{r}{v^{2}}\)
Answer:
(b) \(-\frac{v^{2}}{r}\)

Question 110.
In uniform circular motion –
(a) Speed changes but velocity constant
(b) Velocity changes but speed constant
(c) both speed and velocity are constant
(d) both speed and velocity are variable
Answer:
(b) Velocity changes but speed constant

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Question 111.
In non – uniform circular motion, the resultant acceleration is given by –
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics
Answer:
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics

Question 112.
In non – uniform circular motion, the resultant acceleration makes an angle with the radius vector is –
Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics Q112
Answer:
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics

Question 113.
A compartment of an uniformly moving train is suddenly detached from the train and stops after covering some distance. The distance covered by the compartment and distance covered by the train in the given time –
(a) both will be equal
(b) second will be half of first
(c) first will be half of second
(d) none
Answer:
(c) first will be half of second

Question 114.
An object is dropped from rest. Its v – t graph is –
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics
Answer:
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics

Question 115.
When a ball hits the ground as free fall and renounces but less than its original height? Which is represented by –
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics
Answer:
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics

Question 116.
Which of the following graph represents the equation y = mx – C?
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics
Answer:
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics

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Question 117.
Which of the following graph represents the equation y = mx + C?
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics
Answer:
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics

Question 118.
Which of the following graph represents the equation y = mx?
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics
Answer:
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics

Question 119.
Which of the following graph represents the equation y = -mx + C?
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics
Answer:
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics

SamacheerKalvi.Guru

Question 120.
Which of the following graph represents the equation y = kx2?
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics
Answer:
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics

Question 121.
X = -ky2 is represented by –
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics
Answer:
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics

Question 122.
X = ky2 is represented by –
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics
Answer:
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics

Question 123.
y = kx2 is represented by –
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics
Answer:
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics

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Question 124.
X °∝\(\frac { 1 }{ Y }\) (or) XY = constant is represented by –
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics
Answer:
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics

Question 125.
y = e-kx is represented by –
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics
Answer:
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics

Question 126.
Y = 1 – e-kx is represented by –
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics
Answer:
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics

Question 127.
\(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}\) = 1 is represented by –
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics
Answer:
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics

Question 128.
Let y =f(x) is a function. Its maxima (or) minima can be obtained by –
(a) y = 0
(b) f(x) = 0
(c) \(\frac {dy}{dx}\) = 0
(d) \(\frac{d^{2} y}{d x^{2}}\) = 0
Answer:
(c) \(\frac {dy}{dx}\) = 0

Question 129.
A particle at rest starts moving in a horizontal straight line with uniform acceleration. The ratio of the distance covered during the fourth and the third second is –
(a) \(\frac {4}{ 3 }\)
(b) \(\frac { 26 }{ 9 }\)
(e) \(\frac { 7}{ 5 }\)
(d) 2
Answer:
(c) The distance travelled during nth second –
Sn  = u + \(\frac { 1 }{ 2 }\) a (2n -1)
Distance travelled during 4th second S1 = \(\frac { 1 }{ 2 }\) (8 – 1)
Distance travelled during 3rd second S2 = \(\frac { 1 }{ 2 }\) a(6 – 1)
\(\frac{\mathrm{S}_{1}}{\mathrm{S}_{2}}\) = \(\frac { 7 }{ 5 }\)

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Question 130.
The distance travelled by a body, falling freely from rest in t = 1s, t = 2s and t = 3s are in the ratio of –
(a) 1 : 2 : 3
(h) 1 : 3 : 5
(c) 1 : 4 : 9
(d) 9 : 4 : 1
Answer:
(c) The distance travelled by a free falling body S = \(\frac { 1 }{ 2 }\) gt2
∴ S α t2
∴ S1 : S2  : S3 : 12 : 22 : 32 = 1 : 4 : 9.

Question 131.
The displacement of the particle along a straight line at time ¡ is given by X = a + ht + ct2 where a, b, c are constants. The acceleration of the particle is-
(a) a
(b) b
(c) c
(d) 2c
Answer:
(d) X = a + bt + ct2
\(\frac { dX }{ dt }\) = v = b + 2ct
Acceleration = \(\frac{d^{2} X}{d t^{2}}\) = 2c.

Question 132.
Two bullets are fired at an angle of θ and (90 – θ) to the horizontal with same speed. The ratio of their times of flight is –
(a) 1 : 1
(b) 1: tan θ
(c) tan θ : 1
(d) tan2 θ : 1
Answer:
(c) Time of flight tf =  \(\frac { 2x sinθ}{ 9 }\)
tf α sinθ
∴ \(\frac{t_{f_{1}}}{t_{f_{2}}}\) = \(\frac { sinθ }{sin (90 – θ) }\) = \(\frac { sinθ }{cos θ }\) = tanθ
\(t_{f_{1}}: t_{f_{2}}\) = tan θ : 1

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Question 133.
A particle moves along a circular path under the action of a force. The work done by the force is –
(a) positive and non zero
(b) zero
(c) negative and non-zero
(d) none
Answer:
(b) zero

Question 134.
For a particle, revolving in a circle with speed, the acceleration of the particle is –
(a) along the tangent
(b) along the radius
(c) along its circumference
(d) zero
Answer:
(b) along the radius

Question 135.
A gun fires two bullets with same velocity at 60° and 30° with horizontal. The bullets strike at the same horizontal distance. The ratio of maximum height for the two bullets is in the ratio of –
(a) 1 : 2
(b) 3 : 1
(c) 2 : 1
(d) 1 : 3
Answer:
(b) 3 : 1
Max height attained hmax = \(\frac{u^{2} \sin ^{2} \theta}{2 g}\)
∴ hmax α sin2 θ i.e hmax α \(\frac { 1-cos2θ}{ 2 }\)
\(\frac{h_{\max 1}}{h_{\max } 2}\) = \(\frac{3 / 2}{1 / 2}\) = 3

Question 136.
A ball is thrown vertically upward. it is a speed of lo m/s. When it has reached one half of its maximum height. I-low high does the ball rise? (g = 10 ms-2)
(a) 5 m
(b) 7 m
(c) 10 m
(d) 12 m
Answer:
(c) 10 m

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Question 137.
A car moves from X to Y with a uniform speed Vn  and returns to Y with a uniform speed Vd The average speed for this round trip is –
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics
Answer:
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics

Question 138.
Two projectiles of same mass and with same velocity are thrown at an angle of 60° and 30° with the horizontal then which of the following will remain same?
(a) time of flight
(b) range of projectile
(c) maximum height reached
(d) all the above
Answer:
(b) range of projectile

Question 139.
A n object of mass 3 kg is at rest. Now a force of \(\overrightarrow{\mathrm{F}}\) = 6 t2\(\hat{i}\) + 4t\(\hat{j}\) is applied on the object, then the velocity of object at t = 3 second is –
(a) 18\(\hat{i}\) + 3 \(\hat{j}\)
(b) 18\(\hat{i}\) + 6\(\hat{j}\)
(c) 3 \(\hat{i}\) + 18\(\hat{j}\)
(d) 18 \(\hat{i}\) + 4\(\hat{j}\)
Answer:
(b) F = 6 t2\(\hat{i}\) + 4t\(\hat{j}\)
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics

Question 140.
The angle for which maximum height and horizontal range are same for a projectile is –
(a) 32°
(b) 48°
(c) 76°
(d) 84°
Answer:
(c) 76°
Hmax = horizontal range
\(\frac{u^{2} \sin ^{2} \theta}{2 g}\) = \(\frac{u^{2} \sin 2 \theta}{g}\)
\(\frac{\sin ^{2} \theta}{2}\) = 2 sin θ cos θ = sin θ = 4 cos θ tan θ = 4 θ = 76°

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Question 141.
A bullet is dropped from some height, when another bullet is fired horizontally from the same height. They will hit the ground –
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics
(a) depends upon mass of bullet
(b) depends upon the observer
(c) one after another
(d) simultaneously
Answer:
(d) simultaneously

Question 142.
From this velocity – time graph, which of the following is correct?
(a) Constant acceleration
(b) Variable acceleration
(c) Constant velocity
(d) Variable acceleration
Answer:
(b) Variable acceleration

Question 143.
When a projectile is at its maximum height, the direction of its velocity and acceleration are –
(a) parallel to each other
(b) perpendicular to each other
(c) anti – parallel to each other
(d) depends on its speed
Answer:
(b) perpendicular to each other

Question 144.
At the highest point of oblique projection, which of the following is correct?
(a) velocity of the projectile is zero
(b) acceleration of the projectile is zero
(c) acceleration of the projectile is vertically downwards
(d) velocity of the projectile is vertically downwards
Answer:
(c) acceleration of the projectile Is vertically downwards

Question 145.
The range of the projectile depends –
(a) The angle of projection
(b) Velocity of projection
(c) g
(d) all the above
Answer:
(d) all the above

Question 146.
A constant force is acting on a particle and also acting perpendicular to the velocity of the particle. The particle describes the motion in a plane. Then –
(a) angular displacement is zero
(b) its velocity is zero
(c) it velocity is constant
(d) it moves in a circular path
Answer:
(d) it moves in a circular path

Question 147.
If a body moving in a circular path with uniform speed, then –
(a) the acceleration is directed towards its center
(b) velocity and acceleration are perpendicular to each other
(c) speed of the body is constant but its velocity is varying
(d) all the above
Answer:
(d) all the above

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Question 148.
A body is projected vertically upward with the velocity y = 3\(\hat{i}\) + 4\(\hat{j}\) ms-1. The maximum height attained by the body is (g 10 ms-2).
(a) 7 m
(b) 1.25 m
(c) 8 m
(d) 0.08 m
Answer:
(b) v = 3\(\hat{i}\) + 4\(\hat{j}\)
Hmax = \(\frac{v^{2} \sin ^{2} \theta}{2 g}\) = \(\frac{v^{2}}{2 g}\) [ θ = 90 ]
v = \(\sqrt{9+16}\)  = \(\sqrt{25}\)
v2 = 25
Hmax = \(\frac{25}{20}\)  = \(\frac { 5 }{ 4 }\) = 1.25 m

Samacheer Kalvi 11th Physics Kinematics Short Answer Questions – I (1 Mark)

Question 1.
What is frame of reference?
Answer:
In a coordinate system, the position of an object is described relative to it, then such a coordinate system is called as frame of reference.

Question 2.
What are the types of motion?
Answer:

  • Linear motion
  • Circular motion
  • Rotational motion
  • Vibratory motion.

Question 3.
What is linear motion? Give example.
Answer:
An object is said to be in linear motion if it moves in a straight line.
Example – an athlete running on a straight track.

Question 4.
What is circular motion? Give example.
Answer:
Circular motion is defined as a motion described by an object traversing a circular path.
Example – The whirling motion of a stone attached to a string.

Question 5.
What is rotational motion? Give example.
Answer:
During a motion every point in the object traverses a circular path about an axis except the points located on the axis, is called as rotational motion.
Example – Spinning of the earth about its own axis.

Question 6.
What is vibratory motion? Give example.
Answer:
If an object or particle executes a to and fro motion about a fixed point, it is said to be in vibratory motion.
Example – Vibration of a string on a guitar.

Question 7.
What is one dimensional motion? Give example.
Answer:
One dimensional motion is the motion of a particle moving along a straight line.
Example –  Motion of a train along a straight railway track.

Question 8.
What is two dimensional motion? Give example.
Answer:
If a particle moving along a curved path in a plane, then it is said to be in two dimensional motion.
Example – Motion of a coin on a carrom board.

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Question 9.
What is three dimensional motion? Give example.
Answer:
If a particle moving in used three dimensional space, then the particle is said to be in three dimensional motion.
E.g. A bird flying in the sky.

Question 10.
Write about the properties of components of vectors.
Answer:
If two vectors \(\overline{\mathrm{A}}\) and \(\overline{\mathrm{B}}\) are equal, then their individual components are also equal. then their individual components are also equal.
Let\(\overline{\mathrm{A}}\) = \(\overline{\mathrm{B}}\)
then Ax  \(\hat{i}\) + Ay \(\hat{j}\) + Az \(\hat{k}\) = Bx \(\hat{i}\) + By \(\hat{j}\) + Bz \(\hat{k}\)
i.e. Ax = Bx, Ay =  By  = Az = Bz

Question 11.
Give an example for scalar product of two vectors.
Answer:
The work done by a force \(\overrightarrow{\mathrm{F}}\) to move an object through a small displacement \(\overrightarrow{\mathrm{dr}}\) then
Work done W = \(\overrightarrow{\mathrm{F}}\) .\(\overrightarrow{\mathrm{dr}}\) (or) W = F dr cos θ

Question 12.
Give any three example for vector product of two vectors.
Answer:

  1. Torque \(\overrightarrow{\mathrm{t}}\) = \(\overrightarrow{\mathrm{r}}\) x \(\overrightarrow{\mathrm{F}}\). Where i is force and \(\overrightarrow{\mathrm{F}}\) is force and \(\overrightarrow{\mathrm{r}}\) position vector of a particle.
  2. Angular momentum \(\overrightarrow{\mathrm{L}}\) = \(\overrightarrow{\mathrm{r}}\) x \(\overrightarrow{\mathrm{P}}\) where \(\overrightarrow{\mathrm{P}}\) is the linear momentum.
  3. Linear velocity \(\overrightarrow{\mathrm{v}}\) = \(\overrightarrow{\mathrm{ω}}\) x \(\overrightarrow{\mathrm{r}}\) where \(\overrightarrow{\mathrm{ω}}\) is angular velocity.

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Question 13.
What is position vector?
Answer:
It is vector which denotes the position of a particle at any instant of time, with respect to some reference frame or coordinate system.
The position \(\overrightarrow{\mathrm{r}}\) vector of the particle at a point P is given by
\(\overrightarrow{\mathrm{r}}\) = x\(\hat{i}\) + y\(\hat{j}\) + z\(\hat{k}\)
where x, y and z are components of \(\overrightarrow{\mathrm{r}}\).

Question 14.
Write a note an momentum.
Answer:
Momentum of a particle is defined as product of mass with velocity. It is denoted as \(\overrightarrow{\mathrm{p}}\) Momentum is also a vector quantity
\(\overrightarrow{\mathrm{r}}\) = m\(\overrightarrow{\mathrm{v}}\)
The direction of momentum is also in the direction of velocity, and the magnitude of momentum is equal to product of mass and speed of the particle.
p = mv
In component form the momentum can be written as
px\(\hat{i}\) + py\(\hat{j}\)+ pz\(\hat{k}\) = mvx\(\hat{i}\) + mvy\(\hat{j}\) + mvz\(\hat{k}\)
Here,
px = x component of momentum and is equal to mvx
Px = y component of momentum and is equal to mvy
Px = z component of momentum and is equal to mvz

Question 15.
“Displacement vector is basically a position vector”. Comment on it.
Answer:
This statement is almost correct only. Because the displacement vector also gives the position of a point just like a position vector. The difference between these two vectors is p. The displacement vector gives the position of a point with respect to a point other than origin but position vector gives the position of a point with respect to origin.

SamacheerKalvi.Guru

Question 16.
Will two dimensional motion with an acceleration only in one dimension?
Answer:
Yes. In oblique projection, the acceleration is acting vertically downward but the object follows a parabolic path.

Question 17.
A foot ball is kicked by a player with certain angle to the horizontal. Is there any point at which velocity is perpendicular to its acceleration.
Answer:
Yes. At its maximum height in the parabolic path vertical velocity is zero but due to horizontal component, velocity acts along horizontally, but acceleration of the

Question 18.
Give any two examples for parallelogram law of vectors.
Answer:

  • the flight of a bird
  • working of a sling.

Question 19.
Why does rubber ball bounce greater heights on hills than in plains?
Answer:
The maximum height attained by the projectile is inversely proportional to acceleration due to gravity. At greater height, acceleration due to gravity will be lesser than plains. So ball can bounce higher in hills than in plains.

Question 20.
Is it possible for body to have variable velocity but constant speed? Give example.
Answer:
Yes, it is possible. In horizontal circular motion the speed of a particle is always constant but due to the variation in direction continuously, the velocity of a particle varies.

SamacheerKalvi.Guru

Question 21.
What is relative velocity?
Answer:
When two objects are moving with different velocities, then the velocity of one object with respect to another object is called relative velocity of an object with respect to another.

Question 22.
What is average acceleration?
Answer:
The average acceleration is defined as the ratio of change in velocity over the time interval
aavg = \(\frac{\Delta \overrightarrow{\mathrm{v}}}{\Delta t}\) It is a vector quantity.

Question 23.
Write a note an instantaneous acceleration.
Answer:
Instantaneous acceleration or acceleration of a particle at time ‘t’ is given by the ratio of change in velocity over ∆t, as ∆t approaches zero.
Acceleration Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics
In other words, the acceleration of the particle at an instant t is equal to rate of change of velocity

(1) Acceleration is a vector quantity. Its SI unit is ms-2 and its dimensional formula is [M°L1 T-2]

(2) Acceleration is positive if its velocity is increasing, and is negative if the velocity is decreasing. The negative acceleration is called retardation or deceleration.

Question 24.
Write an acceleration in terms of its component?
(Or)
Show that the acceleration is the second derivative of position vector with respect to time.
Answer:
in terms of components, we can write,
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics
are the components of instantaneous acceleration. Since each component of velocity is the derivative of the corresponding coordinate, we can express the components ax, ay, and az as
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics
Then the acceleration vector \(\overrightarrow{\mathrm{a}}\) it self is
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics
Thus acceleration is the second derivative of position vector with respect to time.

SamacheerKalvi.Guru

This is free online projectile motion calculator. enter velocity and time value then click on calculate and result will be instant displayed ,this calculator.

Question 25.
What are the examples of projectile motion?
Answer:

  1. An object dropped from window of a moving train.
  2. A bullet fired from a rifle.
  3. A ball thrown in any direction.
  4. A javelin or shot put thrown by an athlete.
  5. A jet of water issuing from a hole near the bottom of a water tank.

Question 26.
Explain projectile motion.
Answer:
A projectile moves under the combined effect of two velocities.

  • A uniform velocity in the horizontal direction, which will not change provided there is no air resistance.
  • A uniformly changing velocity (i.e., increasing or decreasing) in the vertical direction.

There are two types of projectile motion:

  • Projectile given an initial velocity in the horizontal direction (horizontal projection)
  • Projectile given an initial velocity at an angle to the horizontal (angular projection)

To study the motion of a projectile, let us assume that,

  • Air resistance is neglected.
  • The effect due to rotation of Earth and curvature of Earth is negligible.
  • The acceleration due to gravity is constant in magnitude and direction at all points of the motion of the projectile.

Question 27.
What is time of flight?
Answer:
The time taken for the projectile to complete its trajectory or time taken by the projectile to hit the ground is called time of flight.

Question 28.
Under what condition is the average velocity equal the instantaneous velocity?
Answer:
When the body is moving with uniform velocity.

SamacheerKalvi.Guru

Question 29.
Draw Position time graph of two objects, A & B moving along a straight line, when their relative velocity is zero.
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics

Question 30.
Suggest a situation in which an object is accelerated and have constant speed.
Answer:
Uniform Circular Motion.

Question 31.
Two balls of different masses are thrown vertically upward with same initial velocity. Maximum heights attained by them are h1 and h2 respectively what is h1/h2?
Answer:
Same height,
∴  h1/h2 = 1

Question 32.
A car moving with velocity of 50 kmh-1 on a straight road is ahead of a jeep moving with velocity 75 kmh-1 would the relative velocity be altered if jeep is ahead of car?
Answer:
No change.

Question 33.
Which of the two – linear velocity or the linear acceleration gives the direction of motion of a body?
Answer:
Linear velocity.

Question 34.
Will the displacement of a particle change on changing the position of origin of the coordinate system?
Answer:
Will not change.

Question 35.
If the instantaneous velocity of a particle is zero, will its instantaneous acceleration be necessarily zero?
Answer:
No. (highest point of vertical upward motion under gravity).

SamacheerKalvi.Guru

Question 36.
A projectile is fired with Kinetic energy 1 KJ. If the range is maximum, what is its Kinetic energy, at the highest point?
Answer:
Here \(\frac { 1 }{ 2 }\) mv2 =1kJ=1000 J, θ = 45°
At the highest point, K.E. = \(\frac { 1 }{ 2 }\) m(v cos 0)2 = \(\frac { 1 }{ 2 }\)\(\frac{m v^{2}}{2}\) = \(\frac {1000}{ 2 }\) = 500 J.

Question 37.
Write an example of zero vector.
Answer:
The velocity vectors of a stationary object is a zero vectors.

Question 38.
State the essential condition for the addition of vectors.
Answer:
They must represent the physical quantities of same native.

Question 39.
When is the magnitude of (\(\overline{\mathrm{A}}\) + \(\overline{\mathrm{B}}\)) equal to the magnitude of (\(\overline{\mathrm{A}}\) – \(\overline{\mathrm{B}}\))?
Answer:
When \(\overline{\mathrm{A}}\) is perpendicular to \(\overline{\mathrm{B}}\).

Question 40.
What is the maximum number of component into which a vector can be resolved?
Answer:
Infinite.

Question 41.
A body projected horizontally moves with the same horizontal velocity although it moves under gravity Why?
Answer:
Because horizontal component of gravity is zero along horizontal direction.

Question 42.
What is the angle between velocity and acceleration at the highest point of a projectile motion?
Answer:
90°.

SamacheerKalvi.Guru

Question 43.
When does

  • height attained by a projectile maximum?
  • horizontal range is maximum?

Answer:

  • Height is maximum at θ = 90
  • Range is maximum at θ = 45.

Question 44.
What is the angle between velocity vector and acceleration vector in uniform circular motion?
Answer:
90°.

Question 45.
A particle is in clockwise uniform circular motion the direction of its acceleration is radially inward. If sense of rotation or particle is anticlockwise then what is the direction of its acceleration?
Answer:
Radial in ward.

Question 46.
A train is moving on a straight track with acceleration a. A passenger drops a stone. What is the acceleration of stone with respect to passenger?
Answer:
\(\sqrt{a^{2}+g^{2}}\) where g = acceleration due to gravity.

Question 47.
What is the average value of acceleration vector in uniform circular motion over one cycle?
Answer:
Null vector.

Question 48.
Does a vector quantity depends upon frame of reference chosen?
Answer:
No.

SamacheerKalvi.Guru

Question 49.
What is the angular velocity of the hour hand of a clock?
Answer:
ω = \(\frac {2π}{ 12 }\) = \(\frac { π }{6}\) rad h-1

Question 50.
What is the source of centripetal acceleration for earth to go round the sun?
Answer:
Gravitation force of sun.

Question 51.
What is the angle between (\(\overrightarrow{\mathrm{A}}\) + \(\overrightarrow{\mathrm{A}}\) ) and (\(\overrightarrow{\mathrm{A}}\) – \(\overrightarrow{\mathrm{A}}\)) ?
Answer:
90°

Samacheer Kalvi 11th Physics Kinematics Short Answer Questions – II (2 Marks)

Question 1.
What are positive and negative acceleration in straight line motion?
Solution:
If speed of an object increases with time, its acceleration is positive. (Acceleration is in the direction of motion) and if speed of an object decreases with time its acceleration is negative (Acceleration is opposite to the direction of motion).

Question 2.
Can a body have zero velocity and still be accelerating? If yes gives any situation.
Solution:
Yes, at the highest point of vertical upward motion under gravity.

Question 3.
The displacement of a body is proportional to t3, where t is time elapsed. What is the nature of acceleration –  time graph of the body?
Solution:
As a α t3 ⇒ s = kt3
Velocity, V = \(\frac { ds }{ dt }\) = 3 kt3
Acceleration, a = \(\frac { dv }{ dt }\) = 3 kt3
i.e., a α t
⇒ motion is uniform, acceleration motion, a – t graph is straight-line.

SamacheerKalvi.Guru

Question 4.
Suggest a suitable physical situation for the following graph.
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics
Solution:
A ball thrown up with some initial velocity rebounding from the floor with reduced speed after each hit.

Question 5.
An object is in uniform motion along a straight line, what will be position time graph for the motion of object, if (i) x0 = positive, v = negative is constant.
(i) x0 = positive, v = negative is |\(\vec{v}\) | constant.
(ii) both x0 and v are negative |\(\vec{v}\) | is constant.
(iii) x0 = negative, v = positive |\(\vec{v}\) | is constant.
(iv) both x0 and v are positive |\(\vec{v}\) | is constant where x0 is position at t = 0.
Solution:
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics

Question 6.
A cyclist starts from centre O of a circular park of radius 1 km and moves along the path OPRQO as shown. If he maintains constant speed of 10 ms-1. What is his acceleration at point R in magnitude & direction?
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics
Solution:
Centripetal acceleration, ac = \(\frac{v^{2}}{r}\) = \(\frac{10^{2}}{1000}\) = 0.1 m/s2 along RO.

Question 7.
What will be the effect on horizontal range of a projectile when its initial velocity is doubled keeping angle of projection same?
Solution:
\(\frac{u^{2} \sin 2 \theta}{g}\) ⇒ R α u2
Range comes four times.

SamacheerKalvi.Guru

Question 8.
The greatest height to which a man can throw a stone is h. What will be the greatest distance upto which he can throw the stone?
Solution:
Maximum height:
H = \(\frac{u^{2} \sin ^{2} \theta}{g}\) ⇒ Hmax = \(\frac{u^{2}}{2g}\) = h (at θ = 90)
Maximum range Rmax = \(\frac{u^{2}}{g}\) = 2h

Question 9.
A person sitting in a train moving at constant velocity throws a ball vertically upwards. How will the ball appear to move to an observer.

  • Sitting inside the train
  • Standing outside the train

Solution:

  • Vertical straight line motion
  • Parabolic path.

Question 10.
A gunman always keep his gun slightly tilted above the line of sight while shooting. Why?
Solution:
Because bullet follow Parabolic trajectory under constant downward acceleration.

Question 11.
Is the acceleration of a particle in circular motion not always towards the center. Explain.
Solution:
No acceleration is towards the center only in case of uniform circular motion.

SamacheerKalvi.Guru

Samacheer Kalvi 11th Physics Kinematics Short Answer Questions – III (3 Marks)

Question 1.
Draw
(a) acceleration – time
(b) velocity – time
(c) Position – time graphs representing motion of an object under free fall. Neglect air resistance.
Solution:
The object falls with uniform acceleration equal to ‘g’
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics

Question 2.
The velocity time graph for a particle is shown in figure. Draw acceleration time graph from it.
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics
Solution:
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics

Question 3.
For an object projected upward with a velocity v0, which comes back to the same point after some time, draw
(i) Acceleration – time graph
(ii) Position – time graph
(iii) Velocity time graph
Solution:
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics

Question 4.
The acceleration of a particle in ms2 is given by a = 3t2 + 2t + 2, where time t is in second. If the particle starts with a velocity v = 2 ms-1 at t = 0, then find the velocity at the end of 2s.
Solution:
Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics Q4

SamacheerKalvi.Guru

Question 5.
At what angle do the two forces (P + Q) and (P – Q) act so that the resultant is \(\sqrt{3 P^{2}+Q^{2}}\)?
Solution:
Use
R = \(\sqrt{3 P^{2}+Q^{2}}\)
R = \(\sqrt{3 \mathrm{P}^{2}+\mathrm{Q}^{2}}\)
A = P + Q
B = P – Q
solve, θ = 60°

Question 6.
A car moving along a straight highway with speed of 126 km h 1 is brought to a stop within a distance of 200 m. What is the retardation of the car (assumed uniform) and how long does it take for the car to stop?
Solution:
Initial velocity of car,
u = 126 kmh-1 = 126 x \(\frac {5}{18}\) ms-1 = 35 ms-1 ………(i)
Since, the car finally comes to rest, v = 0
Distance covered, s = 200 m, a = ?, t = ?
v2 = u2 – 2as
or a = \(\frac{v^{2}-u^{2}}{2 s}\) ………..(ii)
substituting the values from eq. (i) in eq . (ii), we get
a = \(\frac{0-(35)^{2}}{2 \times 200}\) = \(\frac{0-(35)^{2}}{2 \times 200}\)
= \(-\frac{46}{16}\) ms-2 = -3.06 ms-2
Negative sign shows that acceleration in negative which is called retardation, i.e., car is uniformly retarded at – a = 3.06 ms-2.
To find t, let us use the relation
v = u + at
t = \(\frac {v-u}{ a }\)
use a = -3.06 ms-2, v = 0, u = 35 ms-1
∴ t = \(\frac {v-u}{ a }\) = \(\frac {0-35}{ -3.06 }\) = 11.44 s
∴ t = 11.44 sec

SamacheerKalvi.Guru

Samacheer Kalvi 11th Physics Kinematics Long Answer Questions
Question 1.
Explain the types of motion with example.
Answer:
(a) Linear motion:
An object is said to be in linear motion if it moves in a straight line.
Examples:

  • An athlete running on a straight track
  • AA particle falling vertically downwards to the Earth.

(b) Circular motion:
Circular motion is defined as a motion described by an object traversing a circular path.
Examples:

  • The whirling motion of a stone attached to a string.
  • The motion of a satellite around the Earth.
  • These two circular motions are shown in figure.

Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics

(c) Rotational motion:
If any object moves in a rotational motion about an axis, the motion is called ‘rotation’. During rotation every point in the object transverses a circular path about an axis, (except the points located on the axis).
Examples:

  • Rotation of a disc about an axis through its center
  • Spinning of the Earth about its own axis.
  • These two rotational motions are shown in figure

Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics

(d) Vibratory motion:
If an object or particle executes a to-and-fro motion about a fixed point, it is said to be in vibratory motion. This is sometimes also called oscillatory motion.
Examples:

  • Vibration of a string on a guitar
  • Movement of a swing
  • These motions are shown in figure

Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics
Other types of motion like elliptical motion and helical motion are also possible.

Question 2.
What are the different types of vectors? ,
Answer:
1. Equal vectors:
Two vectors A and B are said to be equal when they have equal magnitude and same direction and represent the same physical quantity
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics
(a) Collinear vectors:
Col-linear vectors are those which act along the same line. The angle between them can be 0° or 180°.

(i) Parallel vectors:
If two vectors A and B act in the same direction along the same line or on parallel lines, then the angle between them is 0°. Geometrical representation of parallel vectors.
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics

(ii) Anti-parallel vectors:
Two vectors A and B are said to be anti – parallel when they are in opposite directions along the same line or on parallel lines. Then the angle between them is 180°.
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics
2. Unit vector:
A vector divided by its magnitude is a unit vector. The unit vector for \(\overrightarrow{\mathrm{A}}\) is denoted by \(\widehat{A}\) . It has a magnitude equal to unity or one.
Since, \(\widehat{A}\) = \(\frac{\bar{A}}{A}\) we can write \(\overrightarrow{\mathrm{A}}\) = A\(\widehat{A}\)
Thus, we can say that the unit vector specifies only the direction of the vector quantity.

3. Orthogonal unit vectors:
Let \(\hat{i}\), \(\hat{j}\) and \(\hat{k}\) be three unit vectors which specify the directions along positive x-axis, positive y-axis and positive z-axis respectively. These three unit vectors are directed perpendicular to each other, the angle between any two of them is 90°.\(\hat{i}\), \(\hat{j}\) and \(\hat{k}\) and are examples of orthogonal vectors. Two vectors which are perpendicular to each other are called orthogonal vectors as shown in the figure.
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics

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Question 3.
Explain the concept of relative velocity in one and two dimensional motion.
Answer:
When two objects A and B are moving with different velocities, then the velocity of one object A with respect to another object B is called relative velocity of object A with respect to B.

Case I:
Consider two objects A and B moving with uniform velocities VA and VB, as shown, along straight tracks in the same direction \(\overrightarrow{\mathrm{V}}_{\mathrm{A}}\), \(\overrightarrow{\mathrm{V}}_{\mathrm{B}}\) with respect to ground.
The relative velocity of object A with respect to object B is \(\overrightarrow{\mathrm{V}}_{\mathrm{AB}}\) = \(\overrightarrow{\mathrm{V}}_{\mathrm{A}}\) – \(\overrightarrow{\mathrm{V}}_{\mathrm{B}}\).
The relative velocity of object B with respect to object A is \(\overrightarrow{\mathrm{V}}_{\mathrm{BA}}\) = \(\overrightarrow{\mathrm{V}}_{\mathrm{B}}\) – \(\overrightarrow{\mathrm{V}}_{\mathrm{A}}\) Thus, if two objects are moving in the same direction, the magnitude of relative velocity of one object with respect to another is equal to the difference in magnitude of two velocities.

Case II.
Consider two objects A and B moving with uniform velocities \(\overrightarrow{\mathrm{V}}_{\mathrm{A}}\) and \(\overrightarrow{\mathrm{V}}_{\mathrm{B}}\) along the same straight tracks but opposite in direction.
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics
The relative velocity of an object A with respect to object B is –
\(\overrightarrow{\mathrm{V}}_{\mathrm{AB}}\) = \(\overrightarrow{\mathrm{V}}_{\mathrm{A}}\) – (-\(\overrightarrow{\mathrm{V}}_{\mathrm{B}}\)) = \(\overrightarrow{\mathrm{V}}_{\mathrm{A}}\) + \(\overrightarrow{\mathrm{V}}_{\mathrm{B}}\)

The relative velocity of an object B with respect to object A is
\(\overrightarrow{\mathrm{V}}_{\mathrm{AB}}\) = –\(\overrightarrow{\mathrm{V}}_{\mathrm{A}}\) – \(\overrightarrow{\mathrm{V}}_{\mathrm{A}}\) = – (\(\overrightarrow{\mathrm{V}}_{\mathrm{A}}\) + \(\overrightarrow{\mathrm{V}}_{\mathrm{B}}\))
Thus, if two objects are moving in opposite directions, the magnitude of relative velocity of one object with respect to other is equal to the sum of magnitude of their velocities.

Case III.
Consider the velocities \(\overrightarrow{\mathrm{v}}_{\mathrm{A}}\) and \(\overrightarrow{\mathrm{v}}_{\mathrm{B}}\) at an angle θ between their directions. The relative velocity of A with respect to B, \(\overrightarrow{\mathrm{v}}_{\mathrm{AB}}\) = \(\overrightarrow{\mathrm{v}}_{\mathrm{A}}\) – \(\overrightarrow{\mathrm{v}}_{\mathrm{B}}\)
Then, the magnitude and direction of \(\overrightarrow{\mathrm{v}}_{\mathrm{AB}}\) is given by \(\overrightarrow{\mathrm{v}}_{\mathrm{AB}}\) = \(\sqrt{\vec{v}_{\mathrm{A}}^{2}+\vec{v}_{\mathrm{B}}^{2}-2 v_{\mathrm{A}} v_{\mathrm{B}} \cos \theta}\) and tan β = \(\frac{v_{\mathrm{B}} \sin \theta}{v_{\mathrm{A}}-v_{\mathrm{B}} \cos \theta}\) (Here β is angle between (\(\overrightarrow{\mathrm{v}}_{\mathrm{B}}\) and \(\overrightarrow{\mathrm{v}}_{\mathrm{A}}\))
\(\overrightarrow{\mathrm{v}}_{\mathrm{A}}\) – \(\overrightarrow{\mathrm{v}}_{\mathrm{B}}\) cos θ .

(i) When θ = 0, the bodies move along parallel straight lines in the same direction, We have \(\overrightarrow{\mathrm{v}}_{\mathrm{AB}}\) = (\(\overrightarrow{\mathrm{v}}_{\mathrm{A}}\) – \(\overrightarrow{\mathrm{v}}_{\mathrm{B}}\)) in the direction of \(\overrightarrow{\mathrm{v}}_{\mathrm{A}}\) . Obviously \(\overrightarrow{\mathrm{v}}_{\mathrm{BA}}\) = (\(\overrightarrow{\mathrm{v}}_{\mathrm{B}}\) + \(\overrightarrow{\mathrm{v}}_{\mathrm{A}}\)) in the direction of \(\overrightarrow{\mathrm{v}}_{\mathrm{B}}\).

(ii) When θ = 180°, the bodies move along parallel straight lines in opposite directions,
We have \(\overrightarrow{\mathrm{v}}_{\mathrm{AB}}\) = (\(\overrightarrow{\mathrm{v}}_{\mathrm{A}}\)+ \(\overrightarrow{\mathrm{v}}_{\mathrm{B}}\)) in the direction of \(\overrightarrow{\mathrm{v}}_{\mathrm{A}}\) . Similarly, vBA = (vB + vA) in the direction of \(\overrightarrow{\mathrm{v}}_{\mathrm{B}}\) .

(iii) If the two bodies are moving at right angles to each other, then 0 = 90°. The magnitude of the relative velocity of A with respect to B = \(\overrightarrow{\mathrm{v}}_{\mathrm{AB}}\) = \(\sqrt{v_{\mathrm{A}}^{2}+v_{\mathrm{B}}^{2}}\).

(iv) Consider a person moving horizontally with velocity \(\overrightarrow{\mathrm{V}}_{\mathrm{M}}\) . Let rain fall vertically with velocity \(\overrightarrow{\mathrm{V}}_{\mathrm{R}}\) . An umbrella is held to avoid the rain. Then the relative velocity of the rain with respect to the person is,
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics
which has magnitude
\(\overrightarrow{\mathrm{V}}_{\mathrm{RM}}\) = \(\overrightarrow{\mathrm{V}}_{\mathrm{R}}\) – \(\overrightarrow{\mathrm{V}}_{\mathrm{M}}\)
And direction 0 = tan-1\(\left(\frac{V_{\mathrm{M}}}{\mathrm{V}_{\mathrm{R}}}\right)\) with the vertical as shown in figure.

SamacheerKalvi.Guru

Question 4.
Shows that the path of horizontal projectile is a parabola and derive an expression for
1. Time of flight
2. Horizontal range
3. resultant relative and any instant
4. speed of the projectile when it hits the ground?
Answer:
Consider a projectile, say a ball, thrown horizontally with an initial velocity \(\vec{u}\) from the top of a tower of height h. As the ball moves, it covers a horizontal distance due to its uniform horizontal velocity u, and a vertical downward distance because of constant acceleration due to gravity g. Thus, under the combined effect the ball moves along the path OPA. The motion is in a 2 – dimensional plane. Let the ball take time t to reach the ground at point A, Then the horizontal distance travelled by the ball is x(t) = x, and the vertical distance travelled is y(t) = y.
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics
We can apply the kinematic equations along the x direction and y direction separately. Since this is two-dimensional motion, the velocity will have both horizontal component ux and vertical component uy.

Motion along horizontal direction:
The particle has zero acceleration along x direction. So, the initial velocity ux remains constant throughout the motion. The distance traveled by the projectile at a time t is given by the equation x = uxt +\(\frac { 1 }{ 2 }\) at2 . Since a = 0 along x direction, we have x = uxt ……….(1)

Motion along downward direction:
Here uy = 0 (initial velocity has no downward component), a = g (we choose the + ve y – axis in downward direction), and distance y at time t.
From equation, y = uxt +\(\frac { 1 }{ 2 }\) at2 we get
y = \(\frac { 1 }{ 2 }\) at2 …………..(2)

Substituting the value oft from equation (i) in equation (ii) we have
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics
y = Kx2
where K = \(\frac{g}{2 u_{x}^{2}}\) is constant
Equation (iii) is the equation of a parabola. Thus, the path followed by the projectile is a parabola.

1. Time of Flight:
The time taken for the projectile to complete its trajectory or time taken by the projectile to hit the ground is called time of flight. Consider the example of a tower and projectile. Let h be the height of a tower. Let T be the time taken by the projectile to hit the ground, after being thrown horizontally from the tower.

Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics
We know that sy = uyt + \(\frac { 1 }{ 2 }\) at2 for vertical motion. Here .sy = h, t = T, uy = 0 (i.e., no initial vertical velocity). Then h = \(\frac { 1 }{ 2 }\) gt2 or T = \(\sqrt{\frac{2 h}{g}}\) Thus, the time of flight for projectile motion depends on the height of the tower, but is independent of the horizontal velocity of projection. If one ball falls vertically and another ball is projected horizontally with some velocity, both the balls will reach the bottom at the same time. This is illustrated in the Figure

2. Horizontal range:
The horizontal distance covered by the projectile from the foot of the tower to the point where the projectile hits the ground is called horizontal range.
For horizontal motion, we have
sx = uxt + \(\frac { 1 }{ 2 }\) at2
Here,sx = R (range), ux = u, a = 0 (no horizontal acceleration) T is time of flight. Then horizontal range = uT
Since the time of flight T = \(\sqrt{\frac{2 h}{g}}\) we substitute this and we get the horizontal range of the particle as R = u \(\sqrt{\frac{2 h}{g}}\)
The above equation implies that the range R is directly proportional to the initial velocity u and inversely proportional to acceleration due to gravity g.

3. Resultant Velocity (Velocity of projectile at any time):
At any instant t, the projectile has velocity components along both x-axis and y-axis. The resultant of these two components gives the velocity of the projectile at that instant t, as shown in figure. The velocity component at any t along horizontal (x-axis)
is Vx = Ux + axt
Since, ux = u, ax = 0 , we get
ux = u ax = 0 we get
vx = u
The component of velocity along vertical direction (y – axis) is vy = uy + ayt
Since, uy= 0, ay = g, we get
Vy = gt
Hence the velocity of the particle at any instant is –
v = u\(\hat{i}\) + g\(\hat{j}\)
The speed of the particle at any instant t is given by
v = \(\sqrt{v_{x}^{2}+v_{y}^{2}}\)
v= \(\sqrt{u^{2}+g^{2} t^{2}}\)

Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics

4. Speed of the projectile when it hits the ground:
When the projectile hits the ground after initially thrown horizontally from the top of tower of height h, the time of flight is –
t = \(\sqrt{\frac{2 h}{g}}\)
The horizontal component velocity of the projectile remains the same i.e vx = u.
The vertical component velocity of the projectile at time T is
v = gT = g \(\sqrt{\frac{2 h}{g}}\) = \(\sqrt{\frac{2gh}\)
The speed of the particle when it reaches the ground is
v = \(\sqrt{u^{2}+2 g h}\).

SamacheerKalvi.Guru

Question 5.
Derive the relation between Tangential acceleration and angular acceleration.
Answer:
Consider an object moving along a circle of radius r. In a time ∆t, the object travels in an arc distance As as shown in figure. The corresponding angle subtended is ∆θ
The ∆s can be written in terms of ∆θ
∆s = r∆θ ………(i)
in a time ∆t, we have
\(\frac { ∆s }{ ∆t}\) = t \(\frac { ∆θ }{ ∆t}\) …………(ii)
¡n the limit ∆t – 0, the above equation becomes
\(\frac { ds }{ dt}\) = rω …………….(iii)
Here \(\frac { ds }{ dt}\) is linear speed (y) which is tangential to the circle and co is angular speed.
So equation (iii) becomes.
v r = rω …….(iv)
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics
which gives the relation between linear speed and angular speed.
Eq. (iv) is true only for circular motion. In general the relation between linear and angular velocity is given by
\(\vec{v}\) = \(\vec{\omega} \times \vec{r}\) ………..(v)
For circular motion eq. (y) reduces to eq. (iv) since \(\overrightarrow{\mathrm{ω}}\) and \(\overrightarrow{\mathrm{r}}\)are perpendicular to each other.
Differentiating the eq. (iv) with respect to time, we get (since r is constant)
\(\frac { dv }{ dt}\) = \(\frac { rdv }{ dt}\) = rα
Here \(\frac { dv }{ dt}\) Is the tangential acceleration and is denoted as at = \(\frac {dω}{ dt}\)is the angular acceleration
α. Then eq. (v) becomes
at = rα ………..(vii)

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Samacheer Kalvi 11th Physics Kinematics Numerical Questions

Question 1.
The V – t graphs of two objects make angle 30° and 60° with the time axis. Find the ratio of their accelerations.
Solution:
\(\frac{a_{1}}{a_{2}}\) = \(\frac{tan 30}{tan 60}\) = \(\frac{1 / \sqrt{3}}{\sqrt{3}}\) = \(\frac{1}{3}\) = 1 : 3.

Question 2.
When the angle between two vectors of equal magnitudes is 2n/?>, prove that the magnitude of the resultant is equal to either.
Solution:
R = \(\left(\mathrm{P}^{2}+\mathrm{Q}^{2}+2 \mathrm{PQ} \cos \theta\right)^{1 / 2}\) = \(\left(p^{2}+p^{2}+2 p \cdot p \cos \frac{2 \pi}{3}\right)\) = \(\left[2 p^{2}+2 p^{2}\left(\frac{-1}{2}\right)\right]^{1 / 2}\) = p.

Question 3.
If \(\overline{\mathrm{A}}\) = 3\(\hat{i}\) + 4\(\hat{j}\) and \(\overline{\mathrm{B}}\) = 7\(\hat{i}\) + 24 \(\hat{j}\), find a vector having the same magnitude as \(\overline{\mathrm{B}}\) and parallel to \(\overline{\mathrm{A}}\).
Solution:
\(|\overrightarrow{\mathrm{A}}|=\sqrt{3^{2}+4^{2}}=5\)
also \(|\overrightarrow{\mathrm{B}}|=\sqrt{7^{2}+24^{2}}=25\)
desired vector = \(|\overrightarrow{\mathrm{B}}|\) \(\widehat{A}\) = 25 x \(\frac{3 \hat{i}+4 \hat{j}}{5}\) = 5(3\(\hat{j}\) + 4\(\hat{j}\)) = 15 \(\hat{i}\) + 20\(\hat{j}\).

Question 4.
What is the vector sum of n coplanar forces, each of magnitude F, if each force makes an angle of \(\frac {2 π}{ n }\) with the preceding force?
Solution:
Resultant force is zero.

Question 5.
A car is moving along X- axis. As shown in figure it moves from O to P in 18 seconds and return from P to Q in 6 second. What are the average velocity and average speed of the car in going from

  • O to P
  • From O to P and hack to Q

Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics

Solution:

  • O to P, Average velocity =20 ms-1
  • O to P and back to Q

Average velocity = 10 ms-1
Average speed = 20 ms-1

Question 6.
On a 60 km straight road, a bus travels the first 30 km with a uniform speed of 30 kmh-1 . How fast must the bus travel the next 30 km so as to have average speed of 40 kmh-1 for the entire trip?
Solution:
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics

Question 7.
The displacement x of a particle varies with time as x = 4t2 – 15t + 25. Find the position, velocity and acceleration of the particle at t = O.
Solution:
Position, x = 25 m
Velocity = \(\frac { dx}{dt}\)8t – 15
t = 0, v = 0 – 15 = -15 m/s
acceleration, a = \(\frac { dx}{dt}\) = 8 ms-2

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Question 8.
A driver takes 0.20 second to apply the breaks (reaction time). If he is driving car at a speed of 54 kmh-1 and the breaks cause a deceleration of 6.0 ms-2. Find the distance travelled by car after he sees the need to put the breaks.
Solution:
(distance covered during 0.20 s) + (distance covered until rest)
= (15 x 0.25) + [18.75] = 21.75 m.

Question 9.
From the top of a tower 100 m in height a ball is dropped and at the same time another ball is projected vertically upwards from the ground with a velocity of 25 m/s. Find when and where the two balls will meet? (g = 9.8 m/s)
Solution:
For the ball dropped from the top
x = 4.9 t2…….(i)
For the ball thrown upwards
100 – x =25t – 4.9 t2 …….(ii)
From eq. (i) and (ii)
t = 4s  x = 78.4 m.

Question 10.
A ball thrown vertically upwards with a speed of 19.6 ms-1 from the top of a tower returns to the earth in 6s. Find the height of the tower, (g = 9.8 m/s)
Solution:
s = ut + \(\frac { 1 }{ 2 }\) at2
-h = 19. 6 x 6 + \(\frac { 1 }{ 2 }\) x (-9.8) x (6)2
h = 58.8 m.

Question 11.
Two town A and B are connected by a regular bus service with a bus leaving in either direction every T min. A man cycling with a speed of 20 kmh-1 in the direction A to B notices that a bus goes past him every 18 min in the direction of his motion, and every 6 min in the opposite direction. What is the period T of the bus service and with what speed do the buses ply of the road?
Solution:
V =40 krnh-1 and T = 9 min.

SamacheerKalvi.Guru

Question 12.
A motorboat is racing towards north at 25 kmh-1 and the water current in that region is 10 kmh-1 in the direction of 60° east of south. Find the resultant velocity of the boat.
Solution:
V= 21.8 kmh-1
angle with north, θ = 23.4°.

Question 13.
An aircraft is flying at a height of 3400 m above the ground. If the angle subtended at a ground observation point by the aircraft position 10 second apart is 30°, what is the speed of the aircraft?
Solution:
Speed = 182.2 ms-1

Question 14.
A boat is moving with a velocity (3\(\hat{i}\) -4\(\hat{j}\)) with respect to ground. The water in river is flowing with a velocity (-3\(\hat{i}\) – 4\(\hat{j}\)) with respect to ground. What is the relative velocity of boat with respect to river?
Solution:
\(\overrightarrow{\mathrm{V}}_{\mathrm{BW}}\)= \(\overrightarrow{\mathrm{V}}_{\mathrm{B}}\).

Question 15.
A hiker stands on the edge of a clift 490 m above the ground and throws a stone horizontally with an initial speed of 15 ms-1. Neglecting air resistance, find the time taken by the stone to reach the ground and the speed with which it hits the ground. (g 9.8 ms-2)
Solution:
time = 10 seconds
V = \(\sqrt{\mathrm{V}_{s}^{2}+\mathrm{V}_{Y}^{2}}\) = \(\sqrt{15^{2}+98^{2}}\) = 99.1 m/s-1

Question 16.
A bullet fired at an angle of 30° with the horizontal hits the ground 3 km away. By adjusting the angle of projection, can one hope to hit the target 5 km away ? Assume that the muzzle speed to be fixed and neglect air resistance.
Solution:
Maximum Range = 3.46 km
So it is not possible.

Question 17.
A stone tied to the end of a string 80 cm long is whirled in a horizontal circle with a constant speed. If the stone makes 14 revolutions in 25 seconds, what is the magnitude and direction of acceleration of the stone?
Solution:
\(\frac { 88 }{ 25 }\) rad s-1, \(\frac { 2π}{ T}\) = \(\frac { 2πN}{t}\)
a = 991.2 cm s-2

SamacheerKalvi.Guru

Question 18.
A cyclist is riding with a speed of 27 kmh-1 . As he approaches a circular turn on the road of radius 30 m-2, he applies brakes and reduces his
speed at the constant rate 0.5 ms-2. What is the magnitude and direction of the net acceleration of the cyclist on the circular turn?
Solution:
ac = \(\frac{v^{2}}{r}\) = 0.7ms-2
at = 0.5 ms-2
a = \(\sqrt{a^{2}-a^{2}}\) = 0.86 ms-2
If O is the angle between the net acceleration and the velocity of the cyclist, then
0= tan-1 \(\left(\frac{a_{c}}{a_{\mathrm{T}}}\right)\) = tan-1 = 54°28′

Question 19.
If the magnitude of two vectors are 3 and 4 and their scalar product is 6, find angle between them and also find \(\overrightarrow{\mathrm{A}} \times \overrightarrow{\mathrm{B}}\)|
Solution:
\(\overrightarrow{\mathrm{A}}\).\(\overrightarrow{\mathrm{B}}\) = AB cos θ
|\(\overrightarrow{\mathrm{A}} \times \overrightarrow{\mathrm{B}}\)| = AB sin θ
or 6 = (3 x 4) cos θ = 3 x 4 x 60°
or θ = 60°
= 3 x 4 x \(\frac{\sqrt{3}}{2}\) = \(6 \sqrt{3}\)

Question 20.
Find the value ofA so that the vector \(\overrightarrow{\mathrm{A}}\) = 2 \(\hat{i}\) + \(\hat{j}\) + \(\hat{k}\) and \(\overrightarrow{\mathrm{B}}\) = 4\(\hat{i}\) -2 \(\hat{j}\) +2\(\hat{k}\) are perpendicular to each other.
Solution:
\(\overrightarrow{\mathrm{A}} \perp \overrightarrow{\mathrm{B}}\)
⇒ \(\overrightarrow{\mathrm{A}} \cdot \overrightarrow{\mathrm{B}}\)
⇒ t = 3

SamacheerKalvi.Guru

Question 21.
The velocity time graph of a particle is given by –
Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics

  •  Calculate distance and displacement of particle from given v – t graph.
  • Specify the time for which particle undergone acceleration, retardation and moves with constant velocity.
  • Calculate acceleration, retardation from given v – t graph.
  • Draw acceleration-time graph of given v – t graph.

Solution:
(i) distance = area of ∆OAB + area of trapezium BCDE = 12 + 28 = 40 m
(ii) displacement area of ∆OAB – area of trapezium BCDE = 12 – 28 = – 16 m

  • times acc. \((0 \leq t \leq 4) \) and \((12\leq t \leq 16) \)
  • retardation \((4\leq t \leq 8) \)
  • constant velocity \((8\leq t \leq 12) \)
    Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 2 Kinematics

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Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power

Students can Download Physics Chapter 4 Work, Energy and Power Questions and Answers, Notes Pdf, Samacheer Kalvi 11th Physics Solutions Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power

Samacheer Kalvi 11th Physics Work, Energy and Power Textual Questions Solved

Samacheer Kalvi 11th Physics Work, Energy and Power Multiple Choice Questions
Question 1.
A uniform force of (\(2 \hat{i}+\hat{j}\)) + N acts on a particle of mass 1 kg. The particle displaces from position \((3 \hat{j}+\hat{k})\) m to \((5 \hat{i}+3 \hat{j})\) m. Th e work done by the force on the particle is
[AIPMT model 2013]
(a) 9 J
(b) 6 J
(c) 10 J
(d) 12 J
Answer:
(c) 10 J

Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power

Question 2.
A ball of mass 1 kg and another of mass 2 kg are dropped from a tall building whose height is 80 m. After, a fall of 40 m each towards Earth, their respective kinetic energies will be in the ratio of [AIPMT model 2004]
(a) \(\sqrt{2}\) : 1
(b) 1 : \(\sqrt{2}\)
(c) 2 : 1
(d) 1 : 23
Answer:
(d) 1 : 23

Question 3.
A body of mass 1 kg is thrown upwards with a velocity 20 m s-1. It momentarily comes to rest after attaining a height of 18 m. How much energy is lost due to air friction?
(Take g = 10 ms-2) [AIPMT 2009]
(a) 20 J
(b) 30 J
(c) 40 J
(d) 10 J
Answer:
(a) 20 J

Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power

Question 4.
An engine pumps water continuously through a hose. Water leaves the hose with a velocity v and m is the mass per unit length of the water of the jet. What is the rate at which kinetic energy is imparted to water ? [AIPMT 2009]
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 1
Answer:
(a) \(\frac{1}{2} m v^{2}\)

Question 5.
A body of mass 4 m is lying in xv-plane at rest. It suddenly explodes into three pieces. Two pieces each of mass m move perpendicular to each other with equal speed v the total kinetic energy generated due to explosion is [AIPMT 2014]
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 7
Answer:
(b) \(\frac{3}{2} m v^{2}\)

The potential energy calculator to find how much energy is stored in an object raised off the ground.

Question 6.
The potential energy of a system increases, if work is done
(a) by the system against a conservative force
(b) by the system against a non-conservative force
(c) upon the system by a conservative force
(d) upon the system by a non-conservative force
Answer:
(a) by the system against a conservative force

Question 7.
What is the minimum velocity with which a body of mass m must enter a vertical loop of radius R so that it can complete the loop?
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 8
Answer:
(c) \(\sqrt{5 g R}\)

Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power

Question 8.
The work done by the conservative force for a closed path is
(a) always negative
(b) zero
(c) always positive
(d) not defined
Answer:
(b) zero

Question 9.
If the linear momentum of the obj ect is increased by 0.1 %, then the kinetic energy is increased by
(a) 0.1%
(b) 0.2%
(c) 0.4%
(d) 0.01%
Answer:
(b) 0.2%

Question 10.
If the potential energy of the particle is Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 7031, then force experienced by the particle is
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 16
Answer:
(c) F = -βx

Question 11.
A wind-powered generator converts wind energy into electric energy. Assume that the generator converts a fixed fraction of the wind energy intercepted by its blades into electrical energy. For wind speed v, the electrical power output will be proportional to
(a) v
(b) v2
(c) v3
(d) v4
Answer:
(c) v4

Question 12.
Two equal masses m1 and m2 are moving along the same straight line with velocities 5 ms-1 and -9 ms-1 respectively. If the collision is elastic, then calculate the velocities after the collision of Wj and m2, respectively
(a) -4 ms-1 and 10 ms-1
(b) 10 ms-1 and 0 ms-1
(c) -9 ms-1 and 5 ms-1
(d) 5 ms-1 and 1 ms-1
Answer:
(c) -9 ms-1 and 5 ms-1

Question 13.
A particle is placed at the origin and a force F = kx is acting on it (where k is a positive constant). If U(0) = 0, the graph of U(x) versus x will be (where U is the potential energy function) [IIT 2004]
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 20
Answer:
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 21

Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power

Question 14.
A particle which is constrained to move along x-axis, is subjected to a force in the same direction which varies with the distance x of the particle from the origin as F(x) = -kx + ax3. Here, k and a are positive constants. For x ≥ 0, the functional form of the potential energy U(x) of the particle is [IIT 2002]
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 22
Answer:
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 23

Question 15.
A spring of force constant k is cut into two pieces such that one piece is double the length of the other. Then, the long piece will have a force constant of
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 24
Answer:
(b) \(\frac{3}{2} k\)

Samacheer Kalvi 11th Physics Work, Energy and Power Short Answer Questions

Question 1.
Explain how the definition of work in physics is different from general perception.
Answer:
The term work is used in diverse contexts in daily life. It refers to both physical as well as mental work. In fact, any activity can generally be called as work. But in Physics, the.term work is treated as a physical quantity with a precise definition. Work is said to be done by the force when the force applied on a body displaces it.

Question 2.
Write the various types of potential energy. Explain the formulae.
Answer:
(a) U = mgh
U – Gravitational potential energy
m – Mass of the object,
g – acceleration due to gravity
h – Height from the ground,
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 26
u – Elastic potential energy
k – String constant; x-displacement.
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 27
U – electrostatic potential energy
\(\varepsilon_{0}\) = absolute permittivity
q1, q2 – electric charges

Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power

Question 3.
Write the differences between conservative and non-conservative forces. Give two examples each.
Answer:
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 28

Question 4.
Explain the characteristics of elastic and inelastic collision.
Answer:
In any collision process, the total linear momentum and total energy are always conserved whereas the total kinetic energy need not be conserved always. Some part of the initial kinetic energy is transformed to other forms of energy. This is because, the impact of collisions and deformation occurring due to collisions may in general, produce heat, sound, light etc. By taking these effects into account, we classify the types of collisions as follows:
(a) Elastic collision
(b) Inelastic collision
(a) Elastic collision: In a collision, the total initial kinetic energy of the bodies (before collision) is equal to the total final kinetic energy of the bodies (after collision) then, it is called as elastic collision, i.e.,
Total kinetic energy before collision = Total kinetic energy after collision
(b) Inelastic collision: In a collision, the total initial kinetic energy of the bodies (before collision) is not equal to the total final kinetic energy of the bodies (after collision) then, it is called as inelastic collision, i.e.,
Total kinetic energy before collision ≠ Total kinetic energy after collision
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 261
Even though kinetic energy is not conserved but the total energy is conserved. This is because the total energy contains the kinetic energy term and also a term ∆Q, which includes all the losses that take place during collision. Note that loss in kinetic energy during collision is transformed to another form of energy like sound, thermal, etc. Further, if the two colliding bodies stick together after collision such collisions are known as completely inelastic collision or perfectly inelastic collision. Such a collision is found very often. For example when a clay putty is thrown on a moving vehicle, the clay putty (or Bubblegum) sticks to the moving vehicle and they move together with the same velocity.

Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power

Question 5.
Define the following
(a) Coefficient of restitution
(b) Power
(c) Law of conservation of energy
(d) Loss of kinetic energy in inelastic collision.
Answer:
(a) The ratio of velocity of separation after collision to the velocity of approach before collision
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 281
(b) Power is defined as the rate of work done or energy delivered
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 29
Its unit is watt.
(c) The law of conservation of energy states that energy can neither be created nor destroyed. It may be transformed from one form to another but the total energy of an isolated system remains constant.
(d) In perfectly inelastic collision, the loss in kinetic energy during collision is transformed to another form of energy like sound, thermal, heat, light etc. Let KEi be the total kinetic energy before collision and KEf be the total kinetic energy after collision.
Total kinetic energy before collision,
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 30
Total kinetic energy after Collision,
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 31
Then the loss of kinetic energy is
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 32

Samacheer Kalvi 11th Physics Work, Energy and Power Long Answer Questions

Question 1.
Explain with graphs the difference between work done by a constant force and by a variable force.
Answer:
Work done by a constant force: When a constant force F acts on a body, the small work done (dW) by the force in producing a small displacement dr is given by the relation,
dW = (F cos θ) dr ..(1)
The total work done in producing a displacement from initial position ri to final position rf is,
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 33
The graphical representation of the work done by a constant force is shown in figure given below. The area under the graph shows the work done by the constant force.
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 34
Work done by a variable force: When the component of a variable force F acts on a body, the small work done (dW) by the force in producing a small displacement dr is given by the relation
dW = F cos θ dr [F cos θ is the component of the variable force F]
where, F and θ are variables. The total work done for a displacement from initial position ri to final position rf is given by the relation,
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 35
A graphical representation of the work done by a variable force is shown in figure given below. The area under the graph is the work done by the variable force.
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 36

Question 2.
State and explain work energy principle. Mention any three examples for it.
Answer:
(i) If the work done by the force on the body is positive then its kinetic energy increases.
(ii) If the work done by the force on the body is negative then its kinetic energy decreases.
(iii) If there is no work done by the force on the body then there is no change in its kinetic energy, which means that the body has moved at constant speed provided its mass remains constant.
(iv) When a particle moves with constant speed in a circle, there is no change in the kinetic energy of the particle. So according to work energy principle, the work done by centripetal force is zero.

Question 3.
Arrive at an expression for power and velocity. Give some examples for the same.
Answer:
The work done by a force \(\overrightarrow{\mathrm{F}}\) for a displacement \(d \vec{r}\) is
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 37
Left hand side of the equation (i) can be written as
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 38
Since, velocity is Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 39. Right hand side of the equation (i) can be written as dt
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 391
Substituting equation (ii) and equation (iii) in equation (i), we get
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 40
This relation is true for any arbitrary value of dt. This implies that the term within the bracket must be equal to zero, i.e.,
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 41
Hence power \(\mathrm{P}=\overrightarrow{\mathrm{F}} \cdot \vec{v}\)

Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power

Question 4.
Arrive at an expression for elastic collision in one dimension and discuss various cases.
Answer:
Consider two elastic bodies of masses m1 and m2 moving in a straight line (along positive x direction) on a frictionless horizontal surface as shown in figure given below.
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 42
In order to have collision, we assume that the mass m] moves faster than mass m2 i.e., u1 > u2. For elastic collision, the total linear momentum and kinetic energies of the two bodies before and after collision must remain the same.
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 43
From the law of conservation of linear momentum,
Total momentum before collision (pi) = Total momentum after collision (pf)
m1u1 + m2u2 = m1v1 + m2v2 …(i)
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 44
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 45
This means that for any elastic head on collision, the relative speed of the two elastic bodies after the collision has the same magnitude as before collision but in opposite direction. Further note that this result is independent of mass.
Rewriting the above equation for v1 and v2,
v1 = v2 + u2 – u2 …(vi)
Or v2 = u1 + v1 – u2 …(vii)
To find the final velocities v1 and v2:
Substituting equation (vii) in equation (ii) gives the velocity of as m1 as
m1 (u1 – v1) = m2(u1 + v1 – u2 – u2)
m1 (u1 – y1) = m2 (u1 + + v1  – 2u2)
m1u1 – m1v1 = m2u1 + m2v1 + 2m2u2
m1u1 – m2u1 + 2m2u2 = m1v1 + m2v1
(m1– m2) u1 + 2m2u2 = (m1 + m2) v1
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 46
Similarly, by substituting (vi) in equation (ii) or substituting equation (viii) in equation (vii), we get the final velocity of m2 as
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 47
Case 1: When bodies has the same mass i.e., m1 = m2,
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 48
The equations (x) and (xi) show that in one dimensional elastic collision, when two bodies of equal mass collide after the collision their velocities are exchanged.
Case 2: When bodies have the same mass i.e., m1 = m2 and second body (usually called target) is at rest (u2 = 0),
By substituting m1 = m2 = and u2 = 0 in equations (viii) and equations (ix) we get,
from equation (viii) ⇒ v1 = 0 …(xii)
from equation (ix) ⇒ v2 = u1 ….. (xiii)
Equations (xii) and (xiii) show that when the first body comes to rest the second body moves with the initial velocity of the first body.
Case 3: The first body is very much lighter than the second body
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 49
Dividing numerator and denominator of equation (viii) by m2, we get
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 50
Similarly the numerator and denominator of equation (ix) by m2, we get
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 501
The equation (xiv) implies that the first body which is lighter returns back (rebounds) in the opposite direction with the same initial velocity as it has a negative sign. The equation (xv) implies that the second body which is heavier in mass continues to remain at rest even after collision. For example, if a ball is thrown at a fixed wall, the ball will bounce back from the wall with the same velocity with which it was thrown but in opposite direction.
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 51
Dividing numerator and denominator of equation (xiii) by m1, we get
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 52
The equation (xvi) implies that the first body which is heavier continues to move with the same initial velocity. The equation (xvii) suggests that the second body which is lighter will move with twice the initial velocity of the first body. It means that the lighter body is thrown away from the point of collision.

Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power

Question 5.
What is inelastic collision? In which way it is different from elastic collision. Mention few examples in day to day life for inelastic collision.
Answer:
Inelastic collision: In a collision, the total initial kinetic energy of the bodies (before collision) is not equal to the total final kinetic energy of the bodies (after collision) then, it is called as inelastic collision, i.e.,
Total kinetic energy before collision ≠ Total kinetic energy after collision
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 53
Even though kinetic energy is not conserved but the total energy is conserved. This is because the total energy contains the kinetic energy term and also a term ∆Q, which includes all the losses that take place during collision. Note that loss in kinetic energy during collision is transformed to another form of energy like sound, thermal, etc. Further, if the two colliding bodies stick together after collision such collisions are known as completely inelastic collision or perfectly inelastic collision. Such a collision is found very often. For example when a clay putty is thrown on a moving vehicle, the clay putty (or Bubblegum) sticks to the moving vehicle and they move together with the same velocity.
Difference between Elastic & in elastic collision
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 54

Samacheer Kalvi 11th Physics Numerical Problems

Question 1.
Calculate the work done by a force of 30N in lifting a load of 2 Kg to a height of 10m(g = 10 ms-1)
Answer:
Given: F = 30 N, load (m) = 2 kg; height = 10 m, g = 10 ms-2
Gravitational force F = mg = 30 N
The distance moved h = 10 m
Work done on the object W = Fh = 30 × 10 = 300 J.

Question 2.
A ball with a velocity of 5 ms-1 impinges at angle of 60° with the vertical on a smooth horizontal plane. If the coefficient of restitution is 0.5, find the velocity and direction after the impact.
Answer:
Given: Velocity of ball: 5 ms-1
Angle of inclination with vertical: 60°
Coefficient of restitution = 0.5.
Note: Let the angle reflection is θ’ and the speed after collision is v’. The floor exerts a force on the ball along the normal during the collision. There is no force
parallel to the surface. Thus, the parallel component of the velocity of the ball remains unchanged. This gives
v’ sin θ’ = v sin θ …… (i)
Vertical component with respect to floor = v’ cos θ’ (velocity of separation)
Velocity of approach = v cos θ
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 60
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 601
from (i) and (ii)
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 61
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 62

Question 3.
A bob of mass m is attached to one end of the rod of negligible mass and length r, the other end of which is pivoted freely at a fixed center O as shown in the figure.
What initial speed must be given to the object to reach the top of the circle?
(Hint: Use law of conservation of energy). Is this speed. less or greater than speed obtained in the section 4.2.9?
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 63
Answer:
To get the vertical speed given to the object to reach the top of the circle, law of conservation of energy can be used at a points (1) and (2)
Total energy at 1 = Total energy at 2
∴ Potential energy at point 1 = 0
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 64
from eqn (i)
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 641
In this case bob of mass m is connected with a rod of negligible mass, so the velocity of bob at highest point can be equal to zero i.e. v2 = 0
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 65
The speed of bob obtained here is lesser than the speed obtained in section 4.2.9. It is only because of string is replaced by a massless rod here.

Question 4.
Two different unknown masses A and B collide. A is initially at rest when B has a speed v. After collision B has a speed v/2 and moves at right angles to its original direction of motion. Find the direction in which A moves after collision.
Answer:
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 66

Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power

Question 5.
A bullet of mass 20 g strikes a pendulum of mass 5 kg. The centre of mass of pendulum rises a vertical distance of 10 cm. If the bullet gets embedded into the pendulum, calculate its initial speed.
Answer:
Given: m1 = 20 g = 20 × 10-3 kg; m2 = 5 kg; s = 10 × 10-2 m.
Let the speed of the bullet be v. The common velocity of bullet and pendulum bob is V. According to law of conservation of linear momentum.
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 67
The bob with bullet go up with a deceleration of g = 9.8 ms-2. Bob and bullet come to rest at a height of 10 × 10-2 m.
from III rd equation of motion
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 68

Samacheer Kalvi 11th Physics Conceptual Questions

Question 1.
A spring which in initially in un-stretched condition, is first stretched by a length x and again by a further length x. The work done in the first case W1 is one third of the work done in second case W2. True or false?
Answer:
The amount of work done to stretching distance x
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 691
Total work done in stretching the spring through a distance 2x is
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 701
Extra work required to stretch the additional x distance is
W = W2 – W1 = 4W1 – W1 = 3W1
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 712
Hence it is true

Question 2.
Which is conserved in inelastic collision? Total energy (or) Kinetic energy?
Answer:
In inelastic collision total energy is only conserved but kinetic energy is not conserved. A part of kinetic energy is converted into some other form of energy such as sound, heat energy.
Note: The linear momentum is also conserved.

Question 3.
Is there any net work done by external forces on a car moving with a constant speed along a straight road?
Answer:
If the car moves at constant speed, then there is no change in its kinetic energy. It implies that if there is no change in kinetic energy then there is no work done by the force on the body provided its mass remains constant.

Question 4.
A car starts from rest and moves on a surface with uniform acceleration. Draw the graph of kinetic energy versus displacement. What information you can get from that graph?
Answer:
A car starts from rest and moves with uniform acceleration. The graph between kinetic energy and displacement, is a straight line.
The slope of KE and displacement graph gives net force acting on the car to keep the car with uniform acceleration.
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 72

Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power

Question 5.
A charged particle moves towards another charged particle. Under what conditions the total momentum and the total energy of the system conserved?
Answer:
Coulomb force is acting in between the charged particles Internal force is a conservative force. If no external forces act or the work done by external forces is zero then the mechanical energy of the system and also total linear momentum also remains constant.

Samacheer Kalvi 11th Physics Work, Energy and Power Additional Questions Solved

Samacheer Kalvi 11th Physics Multiple Choice Questions

Question 1.
Thrust and linear momentum
(a) Thrust and linear momentum
(b) Work and energy
(c) Work and power
(d) Power and energy
Answer:
(b) Work and energy

Question 2.
The rate of work done is called as
(a) energy
(b) power
(c) force
(d) mechanical energy
Answer:
(b) power

Question 3.
Unit of work done
(a) Nm
(b) joule
(c) either a or b
(d) none
Answer:
(c) either a or b

Question 4.
Dimensional formula for work done is
(a) MLT-1
(b) ML2T2
(c) M-1L-1T2
(d) ML2T-2
Answer:
(d) ML2T-2

Question 5.
When a body moves on a horizontal direction, the amount of work done by the gravitational force is
(a) positive
(b) negative
(c) zero
(d) infinity
Answer:
(c) zero

Question 6.
The amount of work done by centripetal force on the object moving in a circular path is
(a) zero
(b) infinity
(c) positive
(d) negative
Answer:
(a) zero

Question 7.
The work done by the goal keeper catches the ball coming towards him by applying a force is
(a) positive
(b) negative
(c) zero
(d) infinity
Answer:
(b) negative

Question 8.
If the angle between force and displacement is acute then the work done is
(a) positive
(b) negative
(c) zero
(d) maximum
Answer:
(a) positive

Question 9.
If the force and displacement are perpendicular to each other, then the work done is
(a) positive
(b) negative
(c) zero
(d) maximum
Answer:
(c) zero

Question 10.
If the angle between force and displacement is obtuse, then the work done is
(a) positive
(b) negative
(c) zero
(d) minimum
Answer:
(b) negative

Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power

Question 11.
The area covered under force and displacement graph is
(a) work done
(b) acceleration
(c) power
(d) kinetic energy
Answer:
(a) work done

Question 12.
The capacity to do work is
(a) force
(b) energy
(c) work done
(d) power
Answer:
(b) energy

Question 13.
The energy possessed by a body due to its motion is called as
(a) potential energy
(b) kinetic energy
(c) mechanical energy
(d) none
Answer:
(b) kinetic energy

Question 14.
The energy possessed by the body by virtue of its position is called as
(a) potential energy
(b) kinetic energy
(c) mechanical energy
(d) none
Answer:
(a) potential energy

Question 15.
1 erg is equivalent to
(a) 10-7 J
(b) 1.6 × 10-19 J
(c) 4.186 J
(d) 3.6 × 10-6 J
Answer:
(a) 10-7 J

Question 16.
1 electron volt is equivalent to
(a) 10-7 J
(b) 1.6 × 10-19 J
(c) 4.186 J
(d) 3.6 × 10-6 J
Answer:
(b) 1.6 × 10-19 J

Question 17.
1 kilowatt hour is equivalent to
(a) 10-7 J
(b) 1.6 × 10-19 J
(c) 4.186 J
(d) 3.6 × 10-6 J
Answer:
(d) 3.6 × 10-6 J

Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power

Question 18.
1 calorie is equivalent to
(a) 10-7 J
(b) 1.6 × 10-19 J
(c) 4.186 J
(d) 3.6 × 106 J
Answer:
(c) 4.186 J

Question 19.
The amount of work done by a moving body depends on the
(a) mass of the body
(b) velocity
(c) both (a) and (b)
(d) time
Answer:
(c) both (a) and (b)

Question 20.
The kinetic energy of a body is given by
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 301
Answer:
(a) \(\frac{1}{2} m v^{2}\)

Question 21.
Kinetic energy of the body is always
(a) zero
(b) infinity
(c) negative
(d) positive
Answer:
(d) positive

Question 22.
If the work done by the force on the body is positive then its kinetic energy
(a) increases
(b) decreases
(c) zero
(d) either increases or decreases
Answer:
(a) increases

Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power

Question 23.
If p is the momentum of the particle then its kinetic energy is
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 312
Answer:
(c) \(\frac{\mathbf{p}^{2}}{2 \mathbf{m}}\)

Question 24.
If two objects of masses m1 and m2 (m1 > m2) are moving with the same momentum then the kinetic energy will be greater for
(a) m1
(b) m2
(c) m1 or m2
(d) both will have equal kinetic energy
Answer:
(b) m2

Question 25.
For a given momentum, the kinetic energy is proportional to
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 321
Answer:
(b) \(\frac{1}{\mathrm{m}}\)

Question 26.
Elastic potential energy possessed by a spring is
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 331
Answer:
(c) \(\frac{1}{2}\)kx2

Question 27.
Potential energy stored in the spring depends on
(a) spring constant
(b) mass
(c) gravity
(d) length
Answer:
(b) mass

Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power

Question 28.
Two springs of spring constants k1 and k2 (k1 > k2). If they are stretched by the same force then (u1, u2 are potential energy of the springs) is
(a) u1 > u2
(b) u2 > u1
(c) u1 = u2
(d) u1 ≥ u2
Answer:
(b) u2 > u1

Question 29.
Conservative force is
(a) electrostatic force
(b) magnetic force
(c) gravitational force
(d) all the above
Answer:
(d) all the above

Question 30.
Non conservative force is
(a) frictional force
(b) viscous force
(c) air resistance
(d) all the above
Answer:
(d) all the above

Question 31.
If the work done is completely recoverable, then the force is
(a) conservative
(b) non-conservative
(c) both (a) and (b)
(d) frictional in nature
Answer:
(b) non-conservative

Question 32.
The work done by the conservative forces in a cycle is
(a) zero
(b) one
(c) infinity
(d) having negative value
Answer:
(a) zero

Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power

Question 33.
Negative gradient of potential energy gives
(a) conservative force
(b) non conservative force
(c) kinetic energy
(d) frictional force
Answer:
(a) conservative force

Question 34.
When a particle moving in a vertical circle, the variable is/are
(a) velocity of the particle
(b) tension of the string
(c) both (a) and (b)
(d) mass of the particle
Answer:
(c) both (a) and (b)

Question 35.
Which of the following is zero at the highest point in vertical circular motion?
(a) velocity of the particle
(b) tension of the spring
(c) potential energy
(d) none
Answer:
(a) velocity of the particle

Question 36.
The body must have a speed at highest point in vertical circular motion to stay in the circular path
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 702
Answer:
(a) \(\geq \sqrt{\mathbf{g r}}\)

Question 37.
The body must have a minimum speed of lowermost point in vertical circular motion to complete the circle
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 713
Answer:
(c) \(\geq \sqrt{5 \mathrm{gr}}\)

Question 38.
The rate of work done is
(a) energy
(b) force
(c) power
(d) energy flow
Answer:
(c) power

Question 39.
The unit of power is
(a) J
(b) W
(c) J s-1
(d) both (b) and (c)
Answer:
(d) both (b) and (c)

Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power

Question 40.
One horse power (1 hp) is
(a) 476 W
(b) 674 W
(c) 746 W
(d) 764 W
Answer:
(c) 746 W

Question 41.
The dimension of power is
(a) ML2T-2
(b) ML2T-3
(c) ML-2T2
(d) ML-2T3
Answer:
(b) ML2T-3

Question 42.
kWh is the practical unit of
(a) energy
(b) power
(c) electrical energy
(d) none
Answer:
(a) energy

Question 43.
If a force F is applied on a body and the body moves with velocity v, the power will be
(a) F.V
(b) F/V
(c) FV2
(d) FW2
Answer:
(a) F.V

Question 44.
A body of mass m is thrown vertically upward with a velocity v. The height at which the kinetic energy of the body is one third of its initial value is given by
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 75
Answer:
(c) \(\frac{v^{2}}{6 g}\)
Solution:
Initial Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 76. The loss in K.E will be the gain in potential energy
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 767

Question 45.
A body of mass 5 kg is initially at rest. By applying a force of 20 N at an angle of 60° with horizontal the body is moved to a distance of 4 m. The kinetic energy acquired by the body is
(a) 80 J
(b) 60 J
(c) 40 J
(d) 17.2 J
Answer:
(c) 40 J
Solution:
The work done is equal to its kinetic energy
∴ K.E gained = Fs cos θ = 20 × 4 cos 60° = 40 J.

Question 46.
A bullet is fired normally on an immovable wooden plank of thickness 2 m. It loses 20% of its kinetic energy in penetrating a thickness 0.2 m of the plank. The distance penetrated by the bullet inside the wooden plank is
(a) 0.2 m
(b) 0.8 m
(c) 1 m
(d) 1.5 m
Answer:
(c) 1 m
Solution:
The wood offers a constant retardation. If the bullet loses 20% of its kinetic energy by penetrating 0.2m. it can penetrate further into 4 × 0.2 = 0.8 m with the remaining kinetic energy. So the total distance penetrated by the bullet is 0.2 + 0.8 = 1 m.

Question 47.
Which of the following quantity is conserved in all collision process?
(a) kinetic energy
(b) linear momentum
(c) both (a) and (b)
(d) none.
Answer:
(b) linear momentum

Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power

Question 48.
The kinetic energy is conserved in
(a) elastic collision
(b) inelastic collision
(c) both (a) and (b)
(d) none
Answer:
(a) Elastic collision

Question 49.
The kinetic energy is not conserved in
(a) Elastic collision
(b) In elastic collision
(c) both (a) and (b)
(d) none
Answer:
(b) In elastic collision

Question 50.
In inelastic collision, which is conserved
(a) linear momentum
(b) total energy
(c) both (a) and (b)
(d) none
Answer:
(c) both (a) and (b)

Question 51.
If the two colliding bodies stick together after collision such collisions are
(a) elastic collision
(b) inelastic collision
(c) perfectly inelastic collision
(d) head on collision
Answer:
(c) perfectly inelastic collision

Question 52.
When bubblegum is thrown on a moving vehicle, it sticks is an example for
(a) elastic collision
(b) inelastic collision
(c) perfectly inelastic collision
(d) none
Answer:
(c) perfectly inelastic collision

Question 53.
Elastic collision is due to
(a) conservative force
(b) non conservative force
(c) gravitational force
(d) electrostatic force
Answer:
(b) non conservative force

Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power

Question 54.
Inelastic collision is due to
(a) conservative force
(b) non conservative force
(c) gravitational force
(d) electrostatic force
Answer:
(b) non conservative force

Question 55.
If the velocity of separation is equal to the velocity of approach, then the collision is
(a) conservative force
(b) non conservative force
(c) gravitational force
(d) electrostatic force
Answer:
(a) conservative force

Question 56.
For elastic collision, coefficient of restitution is
(a) 0
(b) 1
(c) 0 < e < 1
(d) ∞
Answer:
(b) 1

Question 57.
For inelastic collision co-efficient of restitution is
(a) 0
(b) 1
(c) 0 < e < 1
(d) ∞
Answer:
(c) 0 < e < 1

Question 58.
For perfectly inelastic collision, coefficient of restitution is
(a) 0
(b) 1
(c) 0 < e < 1
(d) ∞
Answer:
(a) 0

Question 59.
The ratio of velocities of equal masses in an inelastic collision with one of the masses is stationary is
60. A box is dragged across a surface by a rope which makes an angle 45° with the horizontal. The tension in the rope is 100 N when the box is dragged 10 m. The work done is
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 80
Answer:
(a) \(\frac{1-e}{1+e}\)

Question 60.
A box is dragged across a surface by a rope which makes an angle 45° with the horizontal. The
tension in the rope is 100 N when the box is dragged 10 m. The work done is
(a) 707.1 J
(b) 607.1 J
(c) 1414.2 J
(d) 900 J
Answer:
(a) 707.1 J
Solution:
The component of force acting along the surface is T cos θ
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 800
∴ Work done = T cos θ × x
= 10o cos 45° × 10
= 707.1 J

Question 61.
A position dependent force F = (7 – 2x + 3x2) N acts on a small body of mass 2 kg and displaces it from x = 0 to x = 5 m. Work done is
(a) 35 J
(b) 70 J
(c) 135 J
(d) 270 J
Answer:
(c) 135 J
Solution:
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 81

Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power

Question 62.
In gravitational field, the work done in moving a body from one point into another depends on
(a) initial and final positions
(b) distance between them
(c) actual distance covered
(d) velocity of motion
Answer:
(c) initial and final positions

Question 63.
A particle of mass “m” moving with velocity v strikes a particle of mass “2m” at rest and sticks to it. The speed of the combined mass is
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 82
Answer:
(c) \(\frac{v}{3}\)
Solution:
According to conservation of linear momentum
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 83

Question 64.
A force of (\(10 \hat{i}-3 \hat{j}+6 \hat{k}\)) N acts on a body of 5 kg and displaces it from (\(6 \hat{i}+5 \hat{j}-3 \hat{k}\)) to (\(10 \hat{i}-2 \hat{j}+7 k\)) m. The work done is
(a) 100 J
(b) 0
(c) 121 J
(d) none of these
Answer:
(c) 121 J
Solution:
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 84

Question 65.
A 9 kg mass and 4 kg mass are moving with equal kinetic energies. The ratio of their momentum is
(a) 1 : 1
(b) 3 : 2
(c) 2 : 3
(d) 9 : 4.
Answer:
(b) 3 : 2
Solution:
Given that K.E are equal
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 85

Question 66.
If momentum of a body increases by 25% its kinetic energy will increase by
(a) 25%
(b) 50%
(c) 125%
(d) 56.25%
Answer:
(d) 56.25%
Solution:
Let momentum of p1 = 100% momentum of p2 = 125%.
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 86

Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power

Question 67.
A missile fired from a launcher explodes in mid air, its total
(a) kinetic energy increases
(b) momentum increases
(c) kinetic energy decreases
(d) momentum decreases
Answer:
(a) kinetic energy increases

Question 68.
A bullet hits and gets embedded in a wooden block resting on a horizontal friction less surface. Which of the following is conserved?
(a) momentum alone
(b) kinetic energy alone
(c) both momentum and kinetic energy
(d) no quantity is conserved
Answer:
(a) momentum alone

Question 69.
Two balls of equal masses moving with velocities 10 m/s and -7 m/s respectively collide elastically. Their velocities after collision will be
(a) 3 ms-1 and 17 ms-1
(b) -7 ms-1 and 10 ms-1
(c) 10 ms-1 and -7 ms-1
(d) 3 ms-1 and -70 ms-1
Answer:
(b) -7 ms-1 and 10 ms-1

Question 70.
A spring of negligible mass having a force constant of 10 Nm-1 is compressed by a force to a distance of 4 cm. A block of mass 900 g is free to leave the top of the spring. If the spring is released, the speed of the block is
(a) 11.3 ms-1
(b) 13.3 × 101 ms-1
(c) 13.3 × 10-2 ms-1
(d) 13.3 × 10-3 ms-1
Answer:
(c) 13.3 × 10-2 ms-1
Solution:
We know that, the potential energy of the spring = \(\frac{1}{2}\)kx2. Here the potential energy of the spring is converted into kinetic energy of the block.
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 90

Question 71.
A particle falls from a height ftona fixed horizontal plate and rebounds. If e is the coefficient ” of restitution, the total distance travelled by the particle on rebounding when it stops is
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 91
Answer:
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 912
S = h + 2e2h + 2e4h + 2e6h + …..
S = h + 2h (e2 + e4 + e6 +…)
By using binomixal expansion we can write it as
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 92

Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power

Question 72.
If the force F acting on a body as a function of x then the work done in moving a body from x = 1 m to x = 3m is
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 923
(a) 6 J
(b) 4 J
(c) 2.5 J
(d) 1 J
Answer:
(b) 4 J

Question 73.
A boy “A” of mass 50 kg climbs up a staircase in 10 s. Another boy “B” of mass 60 kg climbs up a Same staircase in 15s. The ratio of the power developed by the boys “A” and “B” is
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 93
Answer:
(a) \(\frac{5}{4}\)
Solution:
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 94

Samacheer Kalvi 11th Physics Short Answer Questions

Question 1.
Define work, energy, power.
Answer:
Work: Work is said to be done by the force when the force applied on a body displaces it.
Energy: Energy is defined as the ability to do work.
Power: The rate of work done is called power.

Question 2.
Discuss the possibilities of work done to be zero.
Answer:
Work done is zero in the following cases.
(i) When the force is zero (F = 0). For example, ,a body moving on a horizontal smooth frictionless surface will continue to do so as no force (not even friction) is acting along the plane. (This is an ideal situation.)
(ii) When the displacement is zero (dr = 0). For example, when force is applied on a rigid wall it does not produce any displacement. Hence, the work done is zero as shown in figure.
(iii) When the force and displacement are perpendicular (0 = 90°) to each other, when a body moves on a horizontal direction, the gravitational force (mg) does not work on the body, since it acts at right angles to the displacement as shown in Figure (b). In circular motion the centripetal force does not do work on the object moving on a circle as it is always perpendicular to the displacement as shown in Figure (c).
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 95

Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power

Question 3.
Derive the relation between momentum and kinetic energy.
Answer:
Consider an object of mass m moving with a velocity v. Then its linear momentum is
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 96
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 97
Multiplying both the numerator and denominator of equation (i) by mass m
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 98
where | \(\vec{p}\) | is the magnitude of the momentum. The magnitude of the linear momentum can be obtained by
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 99
Note that if kinetic energy and mass are given, only the magnitude of the momentum can be calculated but not the direction of momentum. It is because the kinetic energy and mass are scalars.

Question 4.
How can an object move with zero acceleration (constant velocity) when the external force is acting on the object?
Answer:
It is possible when there is another force which acts exactly opposite to the external applied force. They both cancel each other and the resulting net force becomes zero, hence the object moves with zero acceleration.

Question 5.
Why should the object be moved at constant velocity when we define potential energy?
Answer:
If the object does not move at constant velocity, then it will have different velocities at the initial and final locations. According to work-kinetic energy theorem, the external force will impart some extra kinetic energy. But we associate potential energy to the forces like gravitational force, spring force and coulomb force. So the external agency should not impart any kinetic energy when the object is taken from initial to final location.

Question 6.
Derive an expression for potential energy near the surface of the earth.
Answer:
The gravitational potential energy (U) at some height h is equal to the amount of work required to take the object from ground to that height h with constant velocity. Let us consider a body of mass m being moved from ground to the height h against the gravitational force as shown.
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 100
The gravitational force \(\overrightarrow{\mathrm{F}}_{g}\) acting on the body is, \(\overrightarrow{\mathrm{F}}_{g}=-m g \hat{j}\) (as Gravitational potential energy the force is in y direction, unit vector \(\hat{j}\) is used). Here, negative sign implies that the force is acting vertically downwards. In order to move the body without acceleration (or with constant velocity), an external applied force \(\overrightarrow{\mathrm{F}}_{a}\), equal in magnitude but opposite to that of gravitational force \(\overrightarrow{\mathrm{F}}_{g}\) has to be applied on the body i.e., \(\overrightarrow{\mathrm{F}}_{a}=-\overrightarrow{\mathrm{F}}_{g}\).
This implies that \(\overrightarrow{\mathrm{F}}_{a}=+m g \hat{j}\). The positive sign implies that the applied force is in vertically upward direction. Hence, when the body is lifted up its velocity remains unchanged and thus its kinetic energy also remains constant.
The gravitational potential energy (U) at some height h is equal to the amount of work required to take the object from the ground to that height h.
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 101
Since the displacement and the applied force are in the same upward direction, the angle between them, θ = 0°. Hence, cos 0° = 1 and | \(\overrightarrow{\mathrm{F}}_{a}\) | = mg and | \(d \vec{r}\) | = dr.
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 102

Question 7.
Explain force displacement graph for a spring.
Answer:
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 7030
Since the restoring spring force and displacement are linearly related as F = – kx, and are opposite in direction, the graph between F and x is a straight line with dwelling only in the second and fourth quadrant as shown in Figure. The elastic potential energy can be easily calculated by drawing a F – x graph. The shaded area (triangle) is the work done by the spring force.
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 103

Question 8.
Explain the potential energy – displacement graph for a spring.
Answer:
A compressed or extended spring will transfer its stored potential energy into kinetic energy of the mass attached to the spring. The potential energy-displacement graph is shown in Figure.
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 105
In a frictionless environment, the energy gets transferred from kinetic to potential and potential to kinetic repeatedly such that the total energy of the system remains constant. At the mean position,
∆KE = ∆U

Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power

Question 9.
Define unit of power.
Answer:
The unit of power is watt. One watt is defined as the power when one joule of work is done in one second.

Question 10.
Define average power and instantaneous power.
Answer:
The average power is defined as the ratio of the total work done to the total time taken.
Pav = total work done/total time taken The instantaneous power is defined as the power delivered at an instant
pinst = dw/dt

Question 11.
Define elastic and inelastic collision.
Answer:
In any collision, if the total kinetic energy of the bodies before collision is equal to the total final kinetic energy of the bodies after collision then it is called as elastic collision.
In a collision the total initial kinetic energy of the bodies before collision is not equal to the . total final kinetic energy of the bodies after collision. Then it is called as inelastic collision.

Question 12.
What will happen to the potential energy of the system.
If (i) Two same charged particles are brought towards each other
(ii) Two oppositely charged particles are brought towards each other.
Answer:
(i) When the same charged particles are brought towards each other, the potential energy of the system will increase. Because work has to be done against the force of repulsion. This work done only stored as potential energy.
(ii) When two oppositely charged particles are brought towards each other, the potential energy of the system will decrease. Because work is done by the force of attraction between the charged particles.

Question 13.
Define the conservative and non-conservative forces. Give examples of each.
Answer:
Conservative force : e.g., Gravitational force, electrostatic force.
Non-Conservative force : e.g., forces of friction, viscosity.

Question 14.
A light body and a heavy body have same linear momentum. Which one has greater K.E ?
Answer:
Lighter body has more K.E. as K.E. = \(\frac{p^{2}}{2 m}\) and for constant p, K.E. \(\propto \frac{1}{m}\)

Question 15.
The momentum of the body is doubled, what % does its K.E change?
Answer:
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 120

Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power

Question 16.
A body is moving along a circular path. How much work is done by the centripetal force?
Answer:
W = FS cos 90° = 0.

Question 17.
Which spring has greater value of spring constant – a hard spring or a delicate spring?
Answer:
Hard spring.

Question 18.
Two bodies stick together after collision. What type of collision is in between these two bodies? .
Answer:
Inelastic collision.

Question 19.
State the two conditions under which a force does not work.
Answer:

  1. Displacement is zero or it is perpendicular to force.
  2. Conservative force moves a body over a closed path.

Question 20.
How will the momentum of a body changes if its K.E. is doubled?
Answer:
Momentum becomes \(\sqrt{2}\) times.

Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power

Question 21.
K.E. of a body is increased by 300 %. Find the % increase in its momentum.
Answer:
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 122

Question 22.
A light and a heavy body have same K.E., which of the two have more momentum and why?
Answer:
Heavier body.

Question 23.
Does the P.E. of a spring decreases or increases when it is compressed or stretched?
Answer:
Increases because W.D. on it when it increases is compressed or stretched.

Question 24.
Name a process in which momentum changes but K.E. does not.
Answer:
Uniform circular motion.

Question 25.
What happens to the P.E. of a bubble when it rises in water?
Answer:
Decreases.

Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power

Question 26.
A body is moving at constant speed over a frictionless surface. What is the work done by the weight of the body?
Answer:
W = 0.

Question 27.
Define spring constant of a spring.
Answer:
It is the restoring force set up in a string per unit extension.

Samacheer Kalvi 11th Physics Short Answer Questions 2 Marks

Question 28.
How much work is done by a coolie walking on a horizontal platform with a load on his head? Explain.
Answer:
W = 0 as his displacement is along the horizontal direction and in order to balance the load on his head, he applies a force on it in the upward direction equal to its weight. Thus angle between force and displacement is zero.

Question 29.
Mountain roads rarely go straight up the slope, but wind up gradually. Why?
Answer:
If roads go straight up then angle of slope 0 would be large so frictional force f = µ mg cos θ would be less and the vehicles may slip. Also greater power would be required.

Question 30.
A truck and a car moving with the same K.E. on a straight road. Their engines are simultaneously switched off which one will stop at a lesser distance?
Answer:
By Work – Energy Theorem,
Loss in K.E. = W.D. against the force × distance of friction
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 125
∴ Truck will stop in a lesser distance because of greater mass.

Question 31.
Is it necessary that work done in the motion of a body over a closed loop is zero for every force in nature? Why?
Answer:
No. W.D. is zero only in case of a conservative force.

Question 32.
How high must a body be lifted to gain an amount of P.E. equal to the K.E. it has when moving at speed 20 ms-1. (The value of acceleration due to gravity at a place is 9.8 ms-2).
Answer:
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 132

Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power

Question 33.
Give an example in which a force does work on a body but fails to change its K.E.
Answer:
When a body is pulled on a rough, horizontal surface with constant velocity. Work is done on the body but K.E. remains unchanged.

Question 34.
A bob is pulled sideway so that string becomes parallel to horizontal and released. Length of the pendulum is 2 m. If due to air resistance loss of energy is 10%, what is the speed with which the bob arrived at the lowest point.
Answer:
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 133

Question 35.
Two springs A and B are identical except that A is harder than B (KA > KB) if these are stretched by the equal force. In which spring will more work be done?
Answer:
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 134
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 135

Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power

Question 36.
Find the work done if a particle moves from position r1 = to a position \((3 \hat{i}+2 \hat{j}-6 \hat{k})\) to a position \(\vec{r}_{2}=(14 \hat{i}+13 \hat{j}-9 \hat{k})\) under the effect of force \(\overrightarrow{\mathrm{F}}=(4 \hat{i}+\hat{j}+3 \hat{k}) \mathrm{N}\)
Answer:
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 138

Question 37.
Spring A and B are identical except that A is stiffer than B, i.e., force constant kA > kB. In which spring is more work expended if they are stretched by the same amount?
Answer:
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 139

Question 38.
A ball at rest is dropped from a height of 12 m. It loses 25% of its kinetic energy in striking the ground, find the height to which it bounces. How do you account for the loss in kinetic energy?
Answer:
If ball bounces to height h’, then
mgh’ = 75% of mgh
∴ h’ = 0.75 h = 9 m.

Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power

Question 39.
Which of the two kilowatt hour or electron volt is a bigger unit of energy and by what factor?
Answer:
kwh is a bigger unit of energy.
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 140

Question 40.
A spring of force constant K is cut into two equal pieces. Calculate force constant of each part.
Answer:
Force constant of each half becomes twice the force constant of the original spring.

Samacheer Kalvi 11th Physics Short Answer Questions 3 Marks

Question 41.
A car of mass 2000 kg is lifted up a distance of 30 m by a crane in 1 min. A second crane does the same job in 2 min. Do the cranes consume the same or different amounts of fuel? What is the power supplied by each crane? Neglect Power dissipation against friction.
Answer:
t1 = 1 min = 60 s, t2 = 2 min = 120 s
W = Fs = mgs = 5.88 × 105 J
As both cranes do same amount of work so both consume same amount of fuel.
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 152

Question 42.
20 J work is required to stretch a spring through 0.1m. Find the force constant of the spring. If the spring is further stretched through 0.1 m, calculate work done.
Answer:
P.E. of spring when stretched through a distance 01m,
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 153
when spring is further stretched through 01m, then P.E. will be :
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 154

Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power

Question 43.
A pump on the ground floor of a building can pump up water to fill a tank of volume 30 m3 in 15 min. If the tank is 40 m above the ground, how much electric power is consumed by the pump. The efficiency of the pump is 30%.
Answer:
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 155

Question 44.
A ball bounces to 80% of its original height. Calculate the mechanical energy lost in each bounce.
Answer:
Let Initial P.E. = mgh
P.E. after first bounce = mg × 80% of h = 0.80 mgh
P.E. lost in each bounce = 0.20 mgh
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 156

Samacheer Kalvi 11th Physics Long Answer Questions

Question 1.
Obtain an expression for the critical vertical of a body revolving in a vertical circle
Answer:
Imagine that a body of mass (m) attached to one end of a massless and inextensible string executes circular motion in a vertical plane with the other end of the string fixed. The length of the string becomes the radius (r) of the circular path (See figure).
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 160
Let us discuss the motion of the body by taking the free body diagram (FBD) at a position where the position vector (\(\vec{r}\)) makes an angle θ with the vertically downward direction and the instantaneous velocity is as shown in Figure.
There are two forces acting on the mass.
1. Gravitational force which acts downward
2. Tension along the string.
Applying Newton’s second law on the mass, in the tangential direction,
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 161
The circle can be divided into four sections A, B, C, D for better understanding of the motion. The four important facts to be understood from the two equations are as follows:
(i) The mass is having tangential acceleration (g sin θ) for all values of θ (except θ = 0°), it is clear that this vertical circular motion is not a uniform circular motion.
(ii) From the equations (ii) and (i) it is understood that as the magnitude of velocity is not a constant in the course of motion, the tension in the string is also not constant.
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 162
Hence velocity cannot vanish, even when the tension vanishes.
These points are to be kept in mind while solving problems related to motion in vertical circle.
To start with let us consider only two positions, say the lowest point 1 and the highest point 2 as shown in Figure for further analysis. Let the velocity of the body at the lowest point 1 be \(\vec{v}_{1}\), at the highest point 2 be \(\vec{v}_{2}\) and \(\vec{v}\) at any other point. The direction of velocity is tangential to the circular path at all points. Let \(\overrightarrow{\mathrm{T}}_{1}\) be the tension in the string at the lowest point and \(\overrightarrow{\mathrm{T}}_{2}\) be , the tension at the highest point and \(\overrightarrow{\mathrm{T}}\) be the tension at any other point. Tension at each point acts towards the center. The tensions and velocities at these two points can be found by applying the law of conservation of energy.
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 163
For the lowest point (1)
When the body is at the lowest point 1, the gravitational force \(m \vec{g}\) which acts on the body (vertically downwards) and another one is the tension \(\overrightarrow{\mathrm{T}}_{1}\), acting vertically upwards, i.e. towards the center. From the equation (ii), we get
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 164
For the highest point (2)
At the highest point 2, both the gravitational force mg on the body and the tension T2 act downwards, i.e. towards the center again.
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 165
From equations (iv) and (ii), it is understood that T1 > T2. The difference in tension T1 – T2 is obtained by subtracting equation (iv) from equation (ii).
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 166
The term Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 7032 can be found easily by applying law of conservation of energy at point 1 and also at point 2.
Note: The tension will not do any work on the mass as the tension and the direction of motion is always perpendicular.
The gravitational force is doing work on the mass, as it is a conservative force the total energy of the mass is conserved throughout the motion.
Total energy at point 1 (E1) is same as the total energy at a point 2 (E2)
E1 = E2
Potential energy at point 1, U1 = 0 (by taking reference as point 1)
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 167
Similarly, Potential energy at point 2, U2 = mg (2r) (h is 2r from point 1)
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 168
From the law of conservation of energy given in equation (vi), we get
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 169
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 170
Substituting equation (vii) in equation (iv) we get,
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 171
Therefore, the difference in tension is
T1 – T2 = 6 mg …(viii)
Minimum speed at the highest point (2)
The body must have a minimum speed at point 2 otherwise, the string will slack before reaching point 2 and the body will not loop the circle. To find this minimum speed let us take the tension T2 = 0 in equation (iv).
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 172
The body must have a speed at point 2, \(v_{2} \geq \sqrt{g r}\) to stay in the circular path.
Maximum speed at the lowest point 1
To have this minimum speed (\(v_{2}=\sqrt{g r}\)) at point 2, the body must have minimum speed also at point 1.
By making use of equation (vii) we can find the minimum speed at point 1.
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 173
Substituting equation (ix) in (vii),
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 174
The body must have a speed at point 1, \(v_{1} \geq \sqrt{5 g r}\) to stay in the circular path.
From equations (ix) and (x), it is clear that the minimum speed at the lowest point 1 should be v 5 times more than the minimum speed at the highest point 2, so that the body loops without leaving the circle.

Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power

Question 2.
Obtain the expressions for the velocities of the two bodies after collision in the case of one dimensional elastic collision and discuss the special cases.
Answer:
Consider two elastic bodies of masses m1 and m2 moving in a straight line (along positive x direction) on a frictionless horizontal surface as shown in figure.
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 180
In order to have collision, we assume that the mass m1 moves faster than mass m2 i.e., u1 > u2.
For elastic collision, the total linear momentum and kinetic energies of the two bodies before and after collision must remain the same
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 181
From the law of conservation of linear momentum,
Total momentum before collision (pi) = Total momentum after collision (pf)
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 182
For elastic collision,
Total kinetic energy before collision KEi = Total kinetic energy after collision KFf
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 183
After simplifying and rearranging the terms,
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 184
Using the formula a2 – b2 = (a + b) (a – b), we can rewrite the above equation as
m1(u1 + v1)(u1 – v1) = m2 (v2 + u2) (v2 – u2) …(iv)
Dividing equation (iv) by (ii) gives,
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 185
This means that for any elastic head on collision, the relative speed of the two elastic bodies after the collision has the same magnitude as before collision but in opposite direction. Further note that this result is independent of mass.
Rewriting the above equation for V1 and v2,
v1 = v2 + u2 – u1
Or v2 = u1 + v1 – u1
To find the final velocities v1 and v2 :
Substituting equation (vii) in equation (ii) gives the velocity of m1 as
m1 (u1 – v1 ) = m2 (u1 + v1 – u2 – u2)
m1u1 – m1v1 = m2(u1 + v1 – 2u2)
m1u1 + 2m2u2 = m1v1 + m2v1
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 186
Similarly, by substituting (vi) in equation (ii) or substituting equation (viii) in equation (vii), we get the final velocity of m2 as
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 1901
Case 1: When bodies has the same mass i.e., m1 = m2,
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 191
The equations (x) and (xi) show that in one dimensional elastic collision, when two bodies of equal mass collide after the collision their velocities are exchanged.
Case 2: When bodies have the same mass i.e., m1 = m2 and second body (usually called target) is at rest (u2 = 0),
By substituting m1m2 = and u2 = 0 in equations (viii) and equations (ix) we get, from equation
(viii) ⇒ V1 = 0 …(xii)
from equation (ix) ⇒ v2 = u1 … (xiii)
Equations (xii) and (xiii) show that when the first body comes to rest the second body moves with the initial velocity of the first body.
Case 3: The first body is very much lighter than the second body
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 192
Similarly, Dividing numerator and denominator of equation (ix) by m2, we get
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 193
v2 = 0
The equation (xiv) implies that the first body which is lighter returns back (rebounds) in the opposite direction with the same initial velocity as it has a negative sign. The equation (xv) implies that the second body which is heavier in mass continues to remain at rest even after collision. For example, if a ball is thrown at a fixed wall, the ball will bounce back from the wall with the same velocity with which it was thrown but in opposite direction.
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 194
Similarly,
Dividing numerator and denominator of equation (xiii) by m1, we get
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 195
The equation (xvi) implies that the first body which is heavier continues to move with the same initial velocity. The equation (xvii) suggests that the second body which is lighter will move with twice the initial velocity of the first body. It means that the lighter body is thrown away from the point of collision.

Samacheer Kalvi 11th Physics Numerical Questions

Question 1.
A body is moving along z-axis of a coordinate system under the effect of a constant force F = Find the work done by the force in moving the body a distance of 2 m along z-axis.
Answer:
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 196
\(\mathrm{W}=\overrightarrow{\mathrm{F}} \cdot \overrightarrow{\mathrm{S}}=2 \mathrm{J}\)

Question 2.
Water is pumped out of a well 10 m deep by means of a pump rated 10 KW. Find the efficiency of the motor if 4200 kg of water is pumped out every minute. Take g = 10 m/s2.
Answer:
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 197

Question 3.
A railway carriage of mass 9000 kg moving with a speed of 36 kmph collides with a stationary carriage of same mass. After the collision, the carriages get coupled and move together. What is their common speed after collision? What type of collision is this?
Answer:
m1 = 9000 kg, u1 = 36 km/h = 10 m/s
m2 = 9000 kg, u2 = 0, v = v1 = v2 = ?
By conservation of momentum:
m1u1 + m2u2 = (m1 + m2)v
∴ v = 5 m/s
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 198
As total K.E. after collision < Total K.E. before collision
∴ collision is inelastic

Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power

Question 4.
In lifting a 10 kg weight to a height of 2m, 230 J energy is spent. Calculate the acceleration with which it was raised.
Answer:
W = mgh + mah = m(g + a)h
∴ a = 1.5 m/s2.

Question 5.
A bullet of mass 0.02 kg is moving with a speed of 10 ms-1. It can penetrate 10 cm of a wooden block, and comes to rest. If the thickness of the target would be 6 cm only, find the K.E. of the bullet when it comes out.
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 199
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 200

Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power

Question 6.
A man pulls a lawn roller through a distance of 20 m with a force of 20 kg weight. If he applies the force at an angle of 60° with the ground, calculate the power developed if he takes 1 min in doing so.
Answer:
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 201

Question 7.
A body of mass 0.3 kg is taken up an inclined plane to length 10 m and height 5 m and then allowed to slide down to the bottom again. The coefficient of friction between the body and the plane is 0.15. What is the
(i) work done by the gravitational force over the round trip?
(ii) work done by the applied force over the upward journey?
(iii) work done by frictional force over the round trip?
(iv) kinetic energy of the body at the end of the trip?
How is the answer to (iv) related to the first three answers?
Answer:
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 202
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 203
(i) W = FS = – mg sin θ × h = -14.7 J is the W.D. by gravitational force in moving plane.
W’ = FS = + mg sin θ × h = 14.7 J is the W.D. by gravitational force in moving the body down the inclined plane.
∴ Total W.D. round the trip, W1 = W + W’ = 0
(ii) Force needed to move the body up the inclined plane,
F = mg sin θ + fk = mg sin θ + µkR = mg sin θ + µk mg cos θ
∴ W.D. by force over the upward journey is
W2 = F × l = mg (sin θ + µk cos θ)l = 18.5 J
(iii) W.D. by frictional force over the round trip,
W3 = -fk(l + l) = -2fkl = -2µkcos θ l = -7.6 J
(iv) K.E. of the body at the end of round trip
= W.D. by net force in moving the body down the inclined plane
= (mg sin θ – µkcos θ) l
= 10.9 J
⇒ K.E. of body = net W.D. on the body.

Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power

Question 8.
Two identical 5 kg blocks are moving with same speed of 2 ms-1 towards each other along a frictionless horizontal surface. The two blocks collide, stick together and come to rest. Consider the two blocks as a system. Calculate work done by
(i) external forces and
(ii) Internal forces.
Answer:
Here no external forces are acting on the system so :
\(\overrightarrow{\mathrm{F}}_{\mathrm{ext}}=0 \Rightarrow \mathrm{W}_{\mathrm{ext}}=0\)
According to work-energy theorem :
Total W.D. = Change in K.E.
or Wext + = Final K.E. – Initial K.E.
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 2012

Question 9.
A truck of mass 1000 kg accelerates uniformly from rest to a velocity of 15 ms-1 in 5 seconds. Calculate
(i) its acceleration,
(ii) its gain in K.E.,
(iii) average power of the engine during this period, neglect friction.
Answer:
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 2013

Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power

Question 10.
An elevator which can carry a maximum load of 1800 kg (elevator + passengers) is moving up with a constant speed of 2 ms-1. The frictional force opposing the motion is 4000 N. Determine the minimum power delivered by the motor to the elevator in watts as well as in horse power.
Answer:
Downward force on the elevator is :
F = mg + f = 22000 N
∴ Power supplied by motor to balance this force is :
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 2022

Question 11.
To simulate car accidents, auto manufacturers study the collisions of moving cars with mounted springs of different spring constants. Consider a typical simulation with a car of mass 1000 kg moving with a speed 18.0 kmh-1 on a smooth road and colliding with a horizontally mounted spring of spring constant 6.25 × 10-3 Nm-1. What is the maximum compression of the spring?
Answer:
At maximum compression xm, the K.E. of the car is converted entirely into the P.E. of the spring.
Samacheer Kalvi 11th Physics Solutions Chapter 4 Work, Energy and Power 2031

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Samacheer Kalvi 11th Physics Solutions Chapter 3 Laws of Motion

Students can Download Physics Chapter 3 Laws of Motion Questions and Answers, Notes Pdf, Samacheer Kalvi 11th Physics Solutions Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 11th Physics Solutions Chapter 3 Laws of Motion

Samacheer Kalvi 11th Physics Chapter 3 Laws of Motion Textual Questions Solved

Samacheer Kalvi 11th Physics Laws of Motion Multiple Choice Questions

Question 1.
When a car takes a sudden left turn in the curved road, passengers are pushed towards the right due to
(a) inertia of direction
(b) inertia of motion
(c) inertia of rest
(d) absence of inertia
Answer:
(a) inertia of direction

Question 2.
An object of mass m held against a vertical wall by applying horizontal force F as shown in the figure. The minimum value of the force F is [IIT JEE 1994]
(a) Less than mg
(b) Equal to mg
(c) Greater than mg
(d) Cannot determine
Answer:
(c) Greater than mg

Question 3.
A vehicle is moving along the positive x direction, if sudden brake is applied, then
(a) frictional force acting on the vehicle is along negative x direction
(b) frictional force acting on the vehicle is along positive x direction
(c) no frictional force acts on the vehicle
(d) frictional force acts in downward direction
Answer:
(a) frictional force acting on the vehicle is along negative x direction

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The normal force formula is defined as the force that any surface exerts on any other object.

Question 4.
A book is at rest on the table which exerts a normal force on the book. If this force is considered as reaction force, what is the action force according to Newton’s third law?
(a) Gravitational force exerted by Earth on the book
(b) Gravitational force exerted by the book on Earth
(c) Normal force exerted by the book on the table
(d) None of the above
Answer:
(c) Normal force exerted by the book on the table

Question 5.
Two masses m1 and m2 are experiencing the same force where m1 < m2 The ratio of their acceleration \(\frac{a_{1}}{a_{2}}\) is –
(a) 1
(b) less than 1
(c) greater than 1
(d) all the three cases
Answer:
(c) greater than 1

Question 6.
Choose appropriate free body diagram for the particle experiencing net acceleration along negative y direction. (Each arrow mark represents the force acting on the system).
Samacheer Kalvi 11th Physics Solutions Chapter 3 Laws of Motion
Answer:
Samacheer Kalvi 11th Physics Solutions Chapter 3 Laws of Motion

Question 7.
A particle of mass m sliding on the smooth double inclined plane (shown in figure) will experience –
(a) greater acceleration along the path AB
(b) greater acceleration along the path AC
(c) same acceleration in both the paths
(d) no acceleration in both the paths
Samacheer Kalvi 11th Physics Solutions Chapter 3 Laws of Motion
Answer:
(a) greater acceleration along the path AC

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Question 8.
Two blocks of masses m and 2m are placed on a smooth horizontal surface as shown. In the first case only a force F1  is applied from the left. Later only a force F2  is applied from the right. If the force acting at the interface of the two blocks in the two cases is same, then F1 : F2 is [Physics Olympiad 2016]
Samacheer Kalvi 11th Physics Solutions Chapter 3 Laws of Motion
(a) 1 : 1
(b) 1 : 2
(c) 2 : 1
(d) 1 : 3
Answer:
(c) 2 : 1

Question 9.
Force acting on the particle moving with constant speed is –
(a) always zero
(b) need not be zero
(c) always non zero
(d) cannot be concluded
Answer:
(b) need not be zero

Question 10.
An object of mass m begins to move on the plane inclined at an angle 0. The coefficient of static friction of inclined surface is lay. The maximum static friction experienced by the mass is –
(a) mg
(b) µs mg
(c) µs mg sin θ
(d) µs mg cos θ
Answer:
(d) µs mg cos θ

Question 11.
When the object is moving at constant velocity on the rough surface –
(a) net force on the object is zero
(b) no force acts on the object
(c) only external force acts on the object
(d) only kinetic friction acts on the object
Answer:
(a) net force on the object is zero

Question 12.
When an object is at rest on the inclined rough surface –
(a) static and kinetic frictions acting on the object is zero
(b) static friction is zero but kinetic friction is not zero
(c) static friction is not zero and kinetic friction is zero
(d) static and kinetic frictions are not zero
Answer:
(c) static friction is not zero and kinetic friction is zero

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Question 13.
The centrifugal force appears to exist –
(a) only in inertial frames
(b) only in rotating frames
(c) in any accelerated frame
(d) both in inertial and non-inertial frames
Answer:
(b) only in rotating frames

Question 14.
Choose the correct statement from the following –
(a) Centrifugal and centripetal forces are action reaction pairs
(b) Centripetal forces is a natural force
(c) Centrifugal force arises from gravitational force
(d) Centripetal force acts towards the center and centrifugal force appears to act away from the center in a circular motion
Answer:
(d) Centripetal force acts towards the center and centrifugal force appears to act away from the center in a circular motion

Question 15.
If a person moving from pole to equator, the centrifugal force acting on him –
(a) increases
(b) decreases
(c) remains the same
(d) increases and then decreases
Answer:
(a) increases

Samacheer Kalvi 11th Physics Laws of Motion Short Answer Questions

Question 1.
Explain the concept of inertia. Write two examples each for inertia of motion, inertia of rest and inertia of direction.
Answer:
The inability of objects to move on its own or change its state of motion is called inertia. Inertia means resistance to change its state. There are three types of inertia:
1. Inertia of rest:
The inability of an object to change its state of rest is called inertia of rest.
Example:

  • When a stationary bus starts to move, the passengers experience a sudden backward push.
  • A book lying on the table will remain at rest until it is moved by some external agencies.

2. Inertia of motion:
The inability of an object to change its state of uniform speed (constant speed) on its own is called inertia of motion.
Example:

  • When the bus is in motion, and if the brake is applied suddenly, passengers move forward and hit against the front seat.
  • An athlete running is a race will continue to run even after reaching the finishing point.

3. Inertia of direction:
The inability of an object to change its direction of motion on its own is called inertia of direction.
Example:

  • When a stone attached to a string is in whirling motion, and if the string is cut suddenly, the stone will not continue to move in circular motion but moves tangential to the circle.
  • When a bus moving along a straight line takes a turn to the right. The passengers are thrown towards left.

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Question 2.
State Newton’s second law.
Answer:
The force acting on an object is equal to the rate of change of its momentum –
\(\overline{\mathrm{F}}\) = \(\frac{d \bar{p}}{d t}\)

Question 3.
Define one newton.
Answer:
One newton is defined as the force which acts on 1 kg of mass to give an acceleration 1 ms-2 in the direction of the force.

Question 4.
Show that impulse is the change of momentum.
Answer:
According to Newton’s Second Law
F = \(\frac {dp}{dt}\) i.e. dp = Fdt
Integrate it over a time interval from ti  to tf
Samacheer Kalvi 11th Physics Solutions Chapter 3 Laws of Motion
Pi → initial momentum of the object at ti
Pf → Final momentum of the object at tf
Pf – Pi = ∆p = change in momentum during the time interval ∆t.
\(\int_{t_{i}}^{t_{f}} \mathrm{F} \cdot d t=\mathrm{J}\) is called the impulse.
If the force is constant over the time interval ∆t, then
Samacheer Kalvi 11th Physics Solutions Chapter 3 Laws of Motion
Hence the proof.

Question 5.
Using free body diagram, show that it is easy to pull an object than to push it.
Answer:
When a body is pushed at an arbitrary angle θ [0 to \(\frac {π}{2}\)], the applied force F can be resolved into two components as F sin 0 parallel to the surface and F cos 0 perpendicular to the surface as shown in figure. The total downward force acting on the body is mg + F cos θ. It implies that the normal force acting on the body increases. Since there is no acceleration along the vertical direction the normal force N is equal to
Npush = mg + F cos θ …………(1)
As a result the maximal static friction also increases and is equal to
\(f_{S}^{\max }\) = \(\mu_{r} \mathrm{N}_{\mathrm{push}}\) = µs(mg + F cos θ) ……(2)
Equation (2) shows that a greater force needs to be applied to push the object into motion.
Samacheer Kalvi 11th Physics Solutions Chapter 3 Laws of Motion

When an object is pulled at an angle θ, the applied force is resolved into two components as shown in figure. The total downward force acting on the object is –
Npull = mg – F cos θ ………….(3)
Samacheer Kalvi 11th Physics Solutions Chapter 3 Laws of Motion

Equation (3) shows that the normal force is less than – Npush. From equations (1) and (3), it is easier to pull an object than to push to make it move.

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Question 6.
Explain various types of friction. Suggest a few methods to reduce friction.
Answer:
There are two types of Friction:
(1) Static Friction:
Static friction is the force which opposes the initiation of motion of an object on the surface. The magnitude of static frictional force fs lies between
\(0 \leq f_{s} \leq \mu_{s} \mathrm{N}\)
where, µs – coefficient of static friction
N – Normal force

(2) Kinetic friction:
The frictional force exerted by the surface when an object slides is called as kinetic friction. Also called as sliding friction or dynamic friction,
fk – µkN
where µk – the coefficient of kinetic friction
N – Normal force exerted by the surface on the object

Methods to reduce friction:
Friction can be reduced

  • By using lubricants
  • By using Ball bearings
  • By polishing
  • By streamlining

Question 7.
What is the meaning by ‘pseudo force’?
Answer:
Pseudo force is an apparent force which has no origin. It arises due to the non-inertial nature of the frame considered.

Question 8.
State the empirical laws of static and kinetic friction.
Answer:
The empirical laws of friction are:

  • Friction is independent of surface of contact.
  • Coefficient of kinetic friction is less than coefficient of static friction.
  • The direction of frictional force is always opposite to the motion of one body over the other.
  • Frictional force always acts on the object parallel to the surface on which the objet is placed,
  • The magnitude of frictional force between any two bodies in contact is directly proportional to the normal reaction between them.

Question 9.
State Newton’s third law.
Answer:
Newton’s third law states that for every action there is an equal and opposite reaction.

Question 10.
What are inertial frames?
Answer:
Inertial frame is the one in which if there is no force on the object, the object moves at constant velocity.

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Question 11.
Under what condition will a car skid on a leveled circular road?
Answer:
On a leveled circular road, if the static friction is not able to provide enough centripetal ’force to turn, the vehicle will start to skid
\(\mu_{s}<\frac{v^{2}}{r g}\)

Samacheer Kalvi 11th Physics Laws of Motion Long Answer Questions

Question 1.
Prove the law of conservation of linear momentum. Use it to find the recoil velocity of a gun when a bullet is fired from it.
Answer:
In nature, conservation laws play a very important role. The dynamics of motion of bodies can be analysed very effectively using conservation laws. There are three conservation laws in mechanics. Conservation of total energy, conservation of total linear momentum, and conservation of angular momentum. By combining Newton’s second and third laws, we can derive the law of conservation of total linear momentum. When two particles interact with each other, they exert equal and opposite forces on each other.

The particle 1 exerts force \(\overrightarrow{\mathrm{F}}_{12}\) on particle 2 and particle 2 exerts an exactly equal and opposite force \(\overrightarrow{\mathrm{F}}_{12}\) on particle 1 according to Newton’s third law.
\(\overrightarrow{\mathrm{F}}_{12}\) = –\(\overrightarrow{\mathrm{F}}_{12}\) ……..(1)
In terms of momentum of particles, the force on each particle (Newton’s second law) can be written as –
\(\overrightarrow{\mathrm{F}}_{12}\) = \(\frac{d \vec{p}_{1}}{d t}\) and \(\overrightarrow{\mathrm{F}}_{21}\) = \(\frac{d \vec{p}_{2}}{d t}\) ………(2)
Here \(\vec{p}_{1}\) is the momentum of particle 1 which changes due to the force \(\overrightarrow{\mathrm{F}}_{12}\) exerted by particle 2. Further Po is the momentum of particle \(\vec{p}_{2}\) This changes due to \(\overrightarrow{\mathrm{F}}_{21}\) exerted by particle 1.
Substitute equation (2) in equation (1)
\(\frac{d \vec{p}_{1}}{d t}\) = – \(\frac{d \vec{p}_{2}}{d t}\) …………(3)
\(\frac{d \vec{p}_{1}}{d t}\) + \(\frac{d \vec{p}_{2}}{d t}\) = 0 ………(4)
\(\frac {d}{dt}\)(\(\vec{p}_{1}\) + \(\vec{p}_{2}\)) = 0
It implies that \(\vec{p}_{1}\) + \(\vec{p}_{2}\) = constant vector (always).
\(\vec{p}_{1}\) + \(\vec{p}_{2}\) is the total linear momentum of the two particles (\(\vec{p}_{tot}\) = \(\vec{p}_{1}\) + \(\vec{p}_{2}\)).It is also called as total linear momentum of the system. Here, the two particles constitute the system. From this result, the law of conservation of linear momentum can be stated as follows.

If there are no external forces acting on the system, then the total linear momentum of the system (\(\vec{p}_{tot}\)) is always a constant vector. In other words, the total linear momentum of the system is conserved in time. Here the word ‘conserve’ means that \(\vec{p}_{1}\) and \(\vec{p}_{2}\) can vary, in such a way that \(\vec{p}_{1}\) + \(\vec{p}_{2}\) is a constant vector.

The forces \(\overrightarrow{\mathrm{F}}_{12}\) and \(\overrightarrow{\mathrm{F}}_{21}\) are called the internal forces of the system, because they act only between the two particles. There is no external force acting on the two particles from outside. In such a case the total linear momentum of the system is a constant vector or is conserved.

Meaning of law of conservation of momentum:
1. The Law of conservation of linear momentum is a vector law. It implies that both the magnitude and direction of total linear momentum are constant. In some cases, this total momentum can also be zero.

2. To analyse the motion of a particle, we can either use Newton’s second law or the law of conservation of linear momentum. Newton’s second law requires us to specify the forces involved in the process. This is difficult to specify in real situations. But conservation of linear momentum does not require any force involved in the process. It is convenient and hence important.
Samacheer Kalvi 11th Physics Solutions Chapter 3 Laws of Motion

For example, when two particles collide, the forces exerted by these two particles on each other is difficult to specify. But it is easier to apply conservation of linear momentum during the collision process.

Examples:
Consider the firing of a gun. Here the system is Gun+bullet. Initially the gun and bullet are at rest, hence the total linear momentum of the system is zero. Let \(\vec{p}_{1}\) be the momentum of the bullet and \(\vec{p}_{2}\) the momentum of the gun before firing. Since initially both are at rest,

Samacheer Kalvi 11th Physics Solutions Chapter 3 Laws of Motion
Total momentum before firing the gun is zero, \(\vec{p}_{1}\) + \(\vec{p}_{2}\) = 0.
According to the law of conservation of linear momentum, total linear momentum has to be zero after the firing also.

When the gun is fired, a force is exerted by the gun on the bullet in forward direction. Now the momentum of the bullet changes from \(\vec{p}_{1}\) to \(\vec{p}_{1}\) To conserve the total linear momentum of the system, the momentum of the gun must also change from \(\vec{p}_{2}\) to \(\vec{p}_{2}^{\prime}\). Due to the conservation of linear momentum, \(\vec{p}_{1}\) + \(\vec{p}_{2}^{\prime}\) = 0.

It implies that \(\vec{p}_{1}^{\prime}\)= \(\vec{p}_{2}^{\prime}\), the momentum of the gun is exactly equal, but in the opposite direction to the momentum of the bullet. This is the reason after firing, the gun suddenly moves backward with the momentum (-\(\vec{p}_{2}^{\prime}\)). It is called ‘recoil momentum’. Th is is an example of conservation of total linear momentum.
Samacheer Kalvi 11th Physics Solutions Chapter 3 Laws of Motion

Question 2.
What are concurrent forces? State Lami’s theorem.
Answer:
Concurrent force:
A collection of forces is said to be concurrent, if the lines of forces act at a common point.

Lami’s Theorem:
If a system of three concurrent and coplanar forces is in equilibrium, then Lami’s theorem states that the magnitude of each force of the system is proportional to sine of the angle between the other two forces.
i.e. |\(\overrightarrow{\mathrm{F}}_{1}\)|∝ sin α, |\(\overrightarrow{\mathrm{F}}_{2}\)| ∝ sin β, |\(\overrightarrow{\mathrm{F}}_{2}\)| ∝ sin γ,

Question 3.
Explain the motion of blocks connected by a string in

  1. Vertical motion
  2. Horizontal motion.

Answer:
When objects are connected by strings and When objects are connected by strings and a force F is applied either vertically or horizontally or along an inclined plane, it produces a tension T in the string, which affects the acceleration to an extent. Let us discuss various cases for the same.

Case 1:
Vertical motion:
Consider two blocks of masses m1 and m2 (m1> m2) connected by a light and in-extensible string that passes over a pulley as shown in Figure.

Samacheer Kalvi 11th Physics Solutions Chapter 3 Laws of Motion

Let the tension in the string be T and acceleration a. When the system is released, both the blocks start moving, m2 vertically upward and mk, downward with same acceleration a. The gravitational force m1g on mass m1 is used in lifting the mass m2. The upward direction is chosen as y direction. The free body diagrams of both masses are shown in Figure.
Samacheer Kalvi 11th Physics Solutions Chapter 3 Laws of Motion

Applying Newton’s second law for mass m2 T \(\hat{j}\) – m2 g \(\hat{j}\) = m2 a \(\hat{j}\) The left hand side of the above equation is the total force that acts on m2 and the right hand side is the product of mass and acceleration of m2 in y direction.
By comparing the components on both sides, we get
T = m2 g = m2 a ……….(1)
Similarly, applying Newton’s second law for mass m2
T \(\hat{j}\) – m1 g\(\hat{j}\) = m1a\(\hat{j}\)
As mass m1 moves downward (-\(\hat{j}\)), its acceleration is along (-\(\hat{j}\))
By comparing the components on both sides, we get
T = m1g = -m1a
m1g – T = m1a ………..(2)
Adding equations (1) and (2), we get
m1g – m2g = m1a + m2a
(m1 – m2)g = (m1 + m2)a …………(3)
From equation (3), the acceleration of both the masses is –
a = (\(\frac{m_{1}-m_{2}}{m_{1}+m_{2}}\))g ………..(4)
If both the masses are equal (m1 = m2), from equation (4)
a = 0
This shows that if the masses are equal, there is no acceleration and the system as a whole will be at rest.
To find the tension acting on the string, substitute the acceleration from the equation (4) into the equation (1).
T = m2g = m2(\(\frac{m_{1}-m_{2}}{m_{1}+m_{2}}\))
T = m2g + m2 (\(\frac{m_{1}-m_{2}}{m_{1}+m_{2}}\))g ……….(5)
By taking m2g common in the RHS of equation (5)
Samacheer Kalvi 11th Physics Solutions Chapter 3 Laws of Motion
Equation (4) gives only magnitude of acceleration.
For mass m1, the acceleration vector is given by \(\vec{a}\) = –\(\frac{m_{1}-m_{2}}{m_{1}+m_{2}}\)\(\hat{j}\)
For mass m2, the acceleration vector is given by \(\vec{a}\) = \(\frac{m_{1}-m_{2}}{m_{1}+m_{2}}\) \(\hat{j}\)

Case 2:
Horizontal motion:
In this case, mass m2 is kept on a horizontal table and mass m1, is hanging through a small pulley as shown in figure. Assume that there is no friction on the surface
Samacheer Kalvi 11th Physics Solutions Chapter 3 Laws of Motion
As both the blocks are connected to the un stretchable string, if m1 moves with an acceleration a downward then m2 also moves with the same acceleration a horizontally.
The forces acting on mass m2 are

  • Downward gravitational force (m2g)
  • Upward normal force (N) exerted by the surface
  • Horizontal tension (T) exerted by the string

The forces acting on mass m1 are

  • Downward gravitational force (m1g)
  • Tension (T) acting upwards

The free body diagrams for both the masses is shown in figure.

Samacheer Kalvi 11th Physics Solutions Chapter 3 Laws of Motion
Applying Newton’s second law for m1
T\(\hat{i}\) – m1g\(\hat{j}\) = -m1a\(\hat{j}\) (alongy direction)
By comparing the components on both sides of the above equation,
T – m1g = -m1a …………(1)
Applying Newton’s second law for m2
Ti = m1ai (along x direction)
By comparing the components on both sides of above equation,
T = m2a ………….(2)
There is no acceleration along y direction for m2.
N\(\hat{j}\) – m2g\(\hat{j}\) = 0
By comparing the components on both sides of the above equation
N – m2g = 0
N = m2g ……….(3)
By substituting equation (2) in equation (1), we can find the tension T
m2a – m1g = -m1a
m2a + m1a = m1g
a = \(\frac{m_{1}}{m_{1}+m_{2}}\)g …………(4)
Tension in the string can be obtained by substituting equation (4) in equation (2)
T = \(\frac{m_{1} m_{2}}{m_{1}+m_{2}}\)g ………..(5)

Comparing motion in both cases, it is clear that the tension in the string for horizontal motion is half of the tension for vertical motion for same set of masses and strings. This result has an important application in industries. The ropes used in conveyor belts (horizontal motion) work for longer duration than those of cranes and lifts (vertical motion).

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Question 4.
Briefly explain the origin of friction. Show that in an inclined plane, angle of friction is pqual to angle of repose.
Answer:
If a very gentle force in the horizontal direction is given to an object at rest on the table it does not move. It is because of the opposing force exerted by the surface on the object which resists its motion. This force is called the frictional force. During the time of Newton and Galileo, frictional force was considered as one of the natural forces like gravitational force. But in the twentieth century, the understanding on atoms, electron and protons has changed the perspective.

The frictional force is actually the electromagnetic force between the atoms on the two surfaces. Even well polished surfaces have irregularities on the surface at the microscopic level. The component of force parallel to the inclined plane (mg sin θ) tries to move the object down. The component of force perpendicular to the inclined plane (mg cos θ) is balanced by the Normal force (N).
N = mg cos θ ………(1)

When the object just begins to move, the static friction attains its maximum value
fs = \(f_{s}^{\max }\) = µs N
This friction also satisfies the relation
\(f_{s}^{\max }\) = µs mg sin θ ……….(2)
Equating the right hand side of equations (1) and (2),
(\(f_{s}^{\max }\))/N = sin θ / cos θ
From the definition of angle of friction, we also know that
tan θ = µs ………..(3)
in which θ is the angle of friction.
Thus the angle of repose is the same as angle of friction. But the difference is that the angle of repose refers to inclined surfaces and the angle of friction is applicable to any type of surface.

Question 5.
State Newton’s three laws and discuss their significance.
Answer:
First Law:
Every object continues to be in the state of rest or of uniform motion (constant velocity) unless there is external force acting on it.

Second Law:
The force acting on an object is equal to the rate of change of its momentum

Third Law:
For every action there is an equal and opposite reaction.

Significance of Newton’s Laws:
1. Newton’s laws are vector laws. The equation \(\overline{\mathrm{F}}\) = m\(\overline{\mathrm{a}}\) is a vector equation and essentially it is equal to three scalar equations. In Cartesian coordinates, this equation can be written as Fx\(\hat{i}\) + Fy\(\hat{j}\) + Fz\(\hat{j}\) = max\(\hat{i}\) + may\(\hat{j}\) + maz\(\hat{j}\)
By comparing both sides, the three scalar equations are

Fx = max The acceleration along the x-direction depends only on the component of force acting along the x – direction.
Fy = may The acceleration along the y direction depends only on the component of force acting along the y – direction.
Fz = maz The acceleration along the z direction depends only on the component of force acting along the z – direction.
From the above equations, we can infer that the force acting along y direction cannot alter the acceleration along x direction. In the same way, Fz cannot affect ay and ax. This understanding is essential for solving problems.

2. The acceleration experienced by the body at time t depends on the force which acts on the body at that instant of time. It does not depend on the force which acted on the body before the time t. This can be expressed as
\(\overline{\mathrm{F}}\)(t) = m\(\overline{\mathrm{a}}\)(t)
Acceleration of the object does not depend on the previous history of the force. For example, when a spin bowler or a fast bowler throws the ball to the batsman, once the ball leaves the hand of the bowler, it experiences only gravitational force and air frictional force. The acceleration of the ball is independent of how the ball was bowled (with a lower or a higher speed).

3. In general, the direction of a force may be different from the direction of motion. Though in some cases, the object may move in the same direction as the direction of the force, it is not always true. A few examples are given below.

Case 1:
Force and motion in the same direction:
When an apple falls towards the Earth, the direction of motion (direction of velocity) of the apple and that of force are in the same downward direction as shown in the Figure.
Samacheer Kalvi 11th Physics Solutions Chapter 3 Laws of Motion

Case 2:
Force and motion not in the same direction:
The Moon experiences a force towards the Earth. But it actually moves in elliptical orbit. In this case, the direction of the force is different from the direction of motion as shown in Figure.

Samacheer Kalvi 11th Physics Solutions Chapter 3 Laws of Motion

Case 3:
Force and motion in opposite direction:
If an object is thrown vertically upward, the direction of motion is upward, but gravitational force is downward as shown in the Figure.

Samacheer Kalvi 11th Physics Solutions Chapter 3 Laws of Motion

Case 4:
Zero net force, but there is motion:
When a raindrop gets detached from the cloud it experiences both downward gravitational force and upward air drag force. As it descends towards the Earth, the upward air drag force increases and after a certain time, the upward air drag force cancels the downward gravity. From then on the raindrop moves at constant velocity till it touches the surface of the Earth. Hence the raindrop comes with zero net force, therefore with zero acceleration but with non-zero terminal velocity. It is shown in the Figure

Samacheer Kalvi 11th Physics Solutions Chapter 3 Laws of Motion

4. If multiple forces \(\overrightarrow{\mathrm{F}}_{1}\), \(\overrightarrow{\mathrm{F}}_{2}\), \(\overrightarrow{\mathrm{F}}_{3}\),……. \(\overrightarrow{\mathrm{F}}_{n}\) act on the same body, then the total force (\(\overrightarrow{\mathrm{F}}_{net}\)) is equivalent to the vectorial sum of the individual forces. Their net force provides the acceleration.
\(\overrightarrow{\mathrm{F}}_{net}\) = \(\overrightarrow{\mathrm{F}}_{1}\) + \(\overrightarrow{\mathrm{F}}_{2}\) + \(\overrightarrow{\mathrm{F}}_{3}\) + ……… + \(\overrightarrow{\mathrm{F}}_{n}\)
Samacheer Kalvi 11th Physics Solutions Chapter 3 Laws of Motion
Newton’s second law for this case is –
\(\overrightarrow{\mathrm{F}}_{net}\) = m\(\overline{\mathrm{a}}\)
In this case the direction of acceleration is in the direction of net force.
Example:
Bow and arrow

Samacheer Kalvi 11th Physics Solutions Chapter 3 Laws of Motion

5. Newton’s second law can also be written in the following form.
Since the acceleration is the second derivative of position vector of the body \(\left(\vec{a}=\frac{d^{2} \vec{r}}{d t^{2}}\right)\)
the force on the body is –
\(\overline{\mathrm{F}}\) = m\(\frac{d^{2} \vec{r}}{d t^{2}}\)
From this expression, we can infer that Newton’s second law is basically a second order ordinary differential equation and whenever the second derivative of position vector is not zero, there must be a force acting on the body.

6. If no force acts on the body then Newton’s second law, m = \(\frac{d \vec{v}}{d t}\) = 0
It implies that \(\overline{\mathrm{v}}\) = constant. It is essentially Newton’s first law. It implies that the second law is consistent with the first law. However, it should not be thought of as the reduction of second law to the first when no force acts on the object. Newton’s first and second laws are independent laws. They can internally be consistent with each other but cannot be derived from each other.

7. Newton’s second law is cause and effect relation. Force is the cause and acceleration is the effect. Conventionally, the effect should be written on the left and cause on the right hand side of the equation. So the correct way of writing Newton’s second law is –
m\(\overline{\mathrm{a}}\) = \(\overline{\mathrm{F}}\) or \(\frac{d \vec{p}}{d t}\) = \(\overline{\mathrm{F}}\)

SamacheerKalvi.Guru

Question 6.
Explain the similarities and differences of centripetal and centrifugal forces.
Answer:
Salient features of centripetal and centrifugal forces.
Centripetal Force:

  • It is a real force which is exerted on the body by the external agencies like gravitational force, tension in the string, normal force etc.
  • Acts in both inertial and non-inertial frames
  • It acts towards the axis of rotation or center of the circle in circular motion
    \(\left|\overrightarrow{\mathrm{F}}_{\mathrm{C}_{\mathrm{P}}}\right|\) = mω2r = \(\frac{m v^{2}}{r}\)
  • Real force and has real effects
  • Origin of centripetal force is interaction between two objects.
  • In inertial frames centripetal force has to be included when free body diagrams are drawn.

Centrifugal Force:

  • It is a pseudo force or fictitious force which cannot arise from gravitational force, tension force, normal force etc.
  • Acts only in rotating frames (non-inertial frame)
  • It acts outwards from the axis of rotation or radially outwards from the center of the circular motion
    \(\left|\overrightarrow{\mathrm{I}}_{\mathrm{C}_{\mathrm{f}}}\right|\) = mω2r = \(\frac{m v^{2}}{r}\)
  • Pseudo force but has real effects
  • Origin of centrifugal force is inertia. It does not arise from interaction. In an inertial frame the object’s inertial motion appears as centrifugal force in the rotating frame.
  • In inertial frames there is no centrifugal force. In rotating frames, both centripetal and centrifugal force have to be included when free body diagrams are drawn.

Question 7.
Briefly explain ‘centrifugal force’ with suitable examples.
Answer:
To use Newton’s first and second laws in the rotational frame of reference, we need to include a Pseudo force called centrifugal force. This centrifugal force appears to act on the object with respect to rotating frames.

Circular motion can be analysed from two different frames of reference. One is the inertial frame (which is either at rest or in uniform motion) where Newton’s laws are obeyed. The other is the rotating frame of reference which is a non – inertial frame of reference as it is accelerating.

When we examine the circular motion from these frames of reference the situations are entirely different. To use Newton’s first and second laws in the rotational frame of reference, we need to include a pseudo force called ‘centrifugal force’. This ‘centrifugal force’ appears to act on the object with respect to rotating frames. To understand the concept of centrifugal force, we can take a specific case and discuss as done below.
Samacheer Kalvi 11th Physics Solutions Chapter 3 Laws of Motion

Free body diagram of a particle including the centrifugal force Consider the case of a whirling motion of a stone tied to a string. Assume that the stone has angular velocity ω in the inertial frame (at rest). If the motion of the stone is observed from a frame which is also rotating along with the stone with same angular velocity ω then, the stone appears to be at rest.

This implies that in addition to the inward centripetal force – mω2r there must be an equal and opposite force that acts on the stone outward with value +mω2r . So the total force acting on the stone in a rotating frame is equal to zero (-mω2r + mω2 r = 0). This outward force +mω2r is called the centrifugal force. The word ‘centrifugal’ means ‘flee from center’.

Note that the ‘centrifugal force’ appears to act on the particle, only when we analyse the motion from a rotating frame. With respect to an inertial frame there is only centripetal force which is given by the tension in the rstring. For this reason centrifugal force is called as a ‘pseudo force’. A pseudo force has no origin. It arises due to the non inertial nature of the frame considered. When circular motion problems are solved from a rotating frame of reference, while drawing free body diagram of a particle, the centrifugal force should necessarily be included as shown in the figure.

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Question 8.
Briefly explain ‘rolling friction’.
Answer:
The invention of the wheel plays a crucial role in human civilization. One of the important applications is suitcases with rolling on coasters. Rolling wheels makes it easier than carrying luggage. When an object moves on a surface, essentially it is sliding on it. But wheels move on the surface through rolling motion. In rolling motion when a wheel moves on a surface, the point of contact with surface is always at rest. Since Rolling and kinetic friction the point of contact is at rest, there is no relative motion between the wheel and surface.
Samacheer Kalvi 11th Physics Solutions Chapter 3 Laws of Motion

Hence the frictional fore is very less. At the same time if an object moves without a wheel, there is a relative motion between the object and the surface. As a result frictional force is larger. This makes it difficult to move the object. The figure shows the difference between rolling and kinetic friction. Ideally in pure rolling, motion of the point of contact with the surface should be at rest, but in practice it is not so.

Due to the elastic nature of the surface at the point of contact there will be some deformation on the object at this point on the wheel or surface as shown in figure. Due to this deformation, there will be minimal friction between wheel and surface. It is called ‘rolling friction. In fact, rolling friction’ is much smaller than kinetic friction.

Question 9.
Describe the method of measuring angle of repose.
Answer:
When objects are connected by strings and When objects are connected by strings and a force F is applied either vertically or horizontally or along an inclined plane, it produces a tension T in the string, which affects the acceleration to an extent. Let us discuss various cases for the same.
Samacheer Kalvi 11th Physics Solutions Chapter 3 Laws of Motion

Case 1:
Vertical motion:
Consider two blocks of masses m1 and m2 (m1> m2) connected by a light and in extensible string that passes over a pulley as shown in Figure.

Let the tension in the string be T and acceleration a. When the system is released, both the blocks start moving, m2 vertically upward and mk, downward with same acceleration a. The gravitational force m1g on mass m1 is used in lifting the mass m2. The upward direction is chosen as y direction. The free body diagrams of both masses are shown in Figure.
Samacheer Kalvi 11th Physics Solutions Chapter 3 Laws of Motion

Applying Newton’s second law for mass m2
T \(\hat{j}\) – m2g\(\hat{j}\) = m2a\(\hat{j}\) The left hand side of the above equation is the total force that acts on m2 and the right hand side is the product of mass and acceleration of m2 in y direction.
By comparing the components on both sides, we get
T = m2g = m2a ……….(1)

Similarly, applying Newton’s second law for mass m2
T \(\hat{j}\) – m1g\(\hat{j}\) = m1a\(\hat{j}\)
As mass mj moves downward (-\(\hat{j}\)), its acceleration is along (-\(\hat{j}\))
By comparing the components on both sides, we get
T = m1g = -m1a
m1g – T = m1a ………..(2)

Adding equations (1) and (2), we get
m1g – m2g = m1a + m2a
(m1 – m2)g = (m1 + m2)a …………(3)
From equation (3), the acceleration of both the masses is –
a = (\(\frac{m_{1}-m_{2}}{m_{1}+m_{2}}\))g ………..(4)
If both the masses are equal (m1 = m2), from equation (4)
a = 0
This shows that if the masses are equal, there is no acceleration and the system as a whole will be at rest.
To find the tension acting on the string, substitute the acceleration from the equation (4) into the equation (1).
T = m2g = m2(\(\frac{m_{1}-m_{2}}{m_{1}+m_{2}}\))
T = m2g + m2 (\(\frac{m_{1}-m_{2}}{m_{1}+m_{2}}\))g ……….(5)
By taking m2g common in the RHS of equation (5)
Samacheer Kalvi 11th Physics Solutions Chapter 3 Laws of Motion
Equation (4) gives only magnitude of acceleration
For mass m1, the acceleration vector is given by \(\vec{a}\) = –\(\frac{m_{1}-m_{2}}{m_{1}+m_{2}}\)\(\hat{j}\)
For mass m2, the acceleration vector is given by \(\vec{a}\) = \(\frac{m_{1}-m_{2}}{m_{1}+m_{2}}\) \(\hat{j}\)

Case 2:
Horizontal motion:
In this case, mass m2 is kept on a horizontal table and mass m1, is hanging through a small pulley as shown in figure. Assume that there is no friction on the surface
Samacheer Kalvi 11th Physics Solutions Chapter 3 Laws of Motion
As both the blocks are connected to the un stretchable string, if m1 moves with an acceleration a downward then m2 also moves with the same acceleration a horizontally.
The forces acting on mass m2 are

  1. Downward gravitational force (m2g)
  2. Upward normal force (N) exerted by the surface
  3. Horizontal tension (T) exerted by the string

The forces acting on mass m1 are

  1. Downward gravitational force (m1g)
  2. Tension (T) acting upwards

The free body diagrams for both the masses is shown in figure 2.
Samacheer Kalvi 11th Physics Solutions Chapter 3 Laws of Motion
Applying Newton’s second law for m1
T\(\hat{i}\) – m1g\(\hat{j}\) = -m1a\(\hat{j}\) (alongy direction)
By comparing the components on both sides of the above equation,
T – m1g = -m1a …………(1)
Applying Newton’s second law for m2
T\(\hat{i}\) = m1a\(\hat{i}\) (along x direction)
By comparing the components on both sides of above equation,
T = m2a ………….(2)
There is no acceleration along y direction for m2.
N\(\hat{j}\) – m2g\(\hat{j}\) = 0
By comparing the components on both sides of the above equation
N – m2g = 0
N = m2g ……….(3)
By substituting equation (2) in equation (1), we can find the tension T
m2a – m1g = -m1a
m2a + m1a = m1g
a = \(\frac{m_{1}}{m_{1}+m_{2}}\)g …………(4)
Tension in the string can be obtained by substituting equation (4) in equation (2)
T = \(\frac{m_{1} m_{2}}{m_{1}+m_{2}}\)g ………..(5)

Comparing motion in both cases, it is clear that the tension in the string for horizontal motion is half of the tension for vertical motion for same set of masses and strings. This result has an important application in industries. The ropes used in conveyor belts (horizontal motion) work for longer duration than those of cranes and lifts (vertical motion).

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Question 10.
Explain the need for banking of tracks.
Answer:
In a leveled circular road, skidding mainly depends on the coefficient of static friction py. The coefficient of static friction depends on the nature of the surface which has a maximum limiting value. To avoid this problem, usually the outer edge of the road is slightly raised compared to inner edge. This is called banking of roads or tracks. This introduces an inclination, and the angle is called banking angle. “Let the surface of the road make angle 9 with horizontal surface. Then the normal force makes the same angle 9 with the vertical. When the car takes a turn.Samacheer Kalvi 11th Physics Solutions Chapter 3 Laws of Motion

there are two forces acting on the car:
(a) Gravitational force mg (downwards)
(b) Normal force N (perpendicular to surface)
We can resolve the normal force into two components N cos θ and N sin θ. The component balances the downward gravitational force ‘mg’ and component will provide the necessary centripetal acceleration. By using Newton second law.
Samacheer Kalvi 11th Physics Solutions Chapter 3 Laws of Motion

The banking angle 0 and radius of curvature of the road or track determines the safe speed of the car at the turning. If the speed of car exceeds this safe speed, then it starts to skid outward but frictional force comes into effect and provides an additional centripetal force to prevent the outward skidding.

At the same time, if the speed of the car is little lesser than safe speed, it starts to skid inward and frictional force comes into effect, which reduces centripetal force to prevent inward skidding. However if the speed of the vehicle is sufficiently greater than the correct speed, then frictional force cannot stop the car from skidding.

Question 11.
Calculate the centripetal acceleration of Moon towards the Earth.
Answer:
The centripetal acceleration is given by a = \(\frac{v^{2}}{r}\) This expression explicitly depends on Moon’s speed which is nontrivial. We can work with the formula
ω2Rm = am
am is centripetal acceleration of the Moon due to Earth’s gravity, ω is angular velocity
Rm is the distance between Earth and the Moon, which is 60 times the radius of the Earth.
Rm = 60R = 60 x 6.4 x 106 = 384 x 106 m
As we know the angular velocity ω = \(\frac { 2π}{ T }\) and T = 27.3 days = 27.3 x 24 x 60 x 60 second = 2.358 x 106 sec.
By substituting these values in the formula for acceleration
a6 = \(\frac{\left(4 \pi^{2}\right)\left(384 \times 10^{6}\right)}{\left(2.358 \times 10^{8}\right)^{2}}\) = 0.00272 ms-2

Samacheer Kalvi 11th Physics Laws of Motion Conceptual Questions

Question 1.
Why it is not possible to push a car from inside?
Answer:
While trying to push a car from outside, he pushes the ground backwards at an angle. The ground offers an equal reaction in the opposite direction, so car can be moved. But the person sits inside means car and the person becomes a single system, and the force given will be a internal force. According to Newton’s third law, total internal force acting on the system is zero and it cannot accelerate the system.

Question 2.
There is a limit beyond which the polishing of a surface increases frictional resistance rather than decreasing it why?
Answer:
Friction is a contact force. Friction is directly proportional to area of contact. In the normal surfaces there are bumps to interlock the surfaces in contact. But the surfaces are polished beyond certain limit. The area of contact will be increased and the molecules come closer to each other. It increases electrostatic force between the molecules. As a result it increases friction.

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Question 3.
Can a single isolated force exist in nature? Explain your answer.
Answer:
No. According to Newton’s third law, for every action, there is an equal and opposite reaction. So, whatever case we consider, if there is an action there is always a reaction. So it is impossible.

Question 4.
Why does a parachute descend slowly?
Answer:
A parachute descends slowly because the surface area of parachute is large so that air gives more resistance when it descends down.

Question 5.
When walking on ice one should take short steps. Why?
Answer:
Let R represent the reaction offered by the ground. The vertical component R cos θ will balance the weight of the person and the horizontal component R sin θ will help the person to walk forward.
Now, normal reaction = R cos θ
Friction force = R sin θ
Coefficient of friction, µ = \(\frac {R sin θ}{R cos θ }\) = tan θ
In a long step, θ is more. So tan θ is more. But p has a fixed value. So, there is danger of slipping in a long step.
Samacheer Kalvi 11th Physics Solutions Chapter 3 Laws of Motion

Question 6.
When a person walks on a surface, the frictional force exerted by the surface on the person is opposite to the direction of motion. True or false?
Answer:
False. In frictional force exerted by the surface on the person is in the direction of his motion. Frictional force acts as an external force to move the person. When the person trying to move, he gives a push to ground on the backward direction and by Newton’s third law he is pushed by the ground in the forward direction. Hence frictional force acts along the direction of motion.

SamacheerKalvi.Guru

Question 7.
Can the coefficient of friction be more than one?
Answer:
Yes. The coefficient of friction can be more than one in some cases such as silicone rubber. Coefficient of friction is the ratio of frictional force to normal force, i.e. F = μR. If p is greater than one means frictional force is greater than normal force. But in general case the value is usually between 0 and 1.

Question 8.
Can we predict the direction of motion of a body from the direction of force on it?
Answer:
Yes. The direction of motion is always opposite to the force of kinetic friction. By using the principle of equilibrium, the direction of force of static friction can be determined. When the object is in equilibrium, the frictional force must point in the direction which results as a net force is zero.

Question 9.
The momentum of a system of particles is always conserved. True or false?
Answer:
True. The total momentum of a system of particles is always constant i.e. conserved. When no external force acts on it.

Samacheer Kalvi 11th Physics Laws of Motion Numerical Problems

Question 1.
A force of 50 N act on the object of mass 20 kg. shown in the figure. Calculate the acceleration of the object in x and y directions.
Answer:
Given F = 50 N and m = 20 kg
(1) component of force along x – direction
Fx = F cos θ
= 50 x cos 30° = 43.30 N
ax = \(\frac{F_{x}}{m}\) = \(\frac {43.30}{20}\) =2.165 ms-2

(2) Component of force along y – direction
Fy = F sin θ = 50 sin 30° = 25 N
ay = \(\frac{F_{y}}{m}\) = \(\frac {25}{20}\) = 1.25 ms-2

Samacheer Kalvi 11th Physics Solutions Chapter 3 Laws of Motion

Question 2.
A spider of mass 50 g is hanging on a string of a cob web as shown in the figure. What is the tension in the string?
Answer:
Given m = 50 g, T = ?
Tension in the string T = mg
= 50 x 10-2 x 9.8 = 0.49 N

Question 3.
What is the reading shown in spring balance?
Samacheer Kalvi 11th Physics Solutions Chapter 3 Laws of Motion
Answer:
When a spring balance hung on a rigid support and load is attached at its other end, the weight of the load exerts a force on the rigid support in turn support exerts equal and opposite force on that load, so that balance will be stretched. This is the principle of spring balance. Flence the answer is 4 kg.
Given: m = 2 kg, 0 = 30°.
Resolve the weight into its component as mg sin θ and mg cos θ.
Here mg sin θ acts parallel to the surface
∴ W = mg sin θ
= 2 x 9.8 x sin 30° = 2 x 9.8 x \(\frac {1}{2}\) = 9.8 N

SamacheerKalvi.Guru

Question 4.
The physics books are stacked on each other in the sequence: +1 volumes 1 and 2; +2 volumes 1 and 2 on a table
(a) Identify the forces acting on each book and draw the free body diagram.
(b) Identify the forces exerted by each book on the other.
Answer:
Let m1, m2, m3, m4, are the masses of +1 volume I and II and +2 volumes I & II
Samacheer Kalvi 11th Physics Solutions Chapter 3 Laws of Motion

(a) Force on book m4

  • Downward gravitational force acting downward (m3g)
  • Upward normal force (N3) exerted by book of mass m3
    Samacheer Kalvi 11th Physics Solutions Chapter 3 Laws of Motion |

(b) Force on book m3

  • Downward gravitational force (m3g)
  • Downward force exerted by m4 (N4)
  • Upward force exerted by m2 (N2)
    Samacheer Kalvi 11th Physics Solutions Chapter 3 Laws of Motion

(c) Force on book m2

  • Downward gravitational force (m2g)
  • Downward force exerted by m3 (N3)
  • Upward force exerted by m1 (CN1)
    Samacheer Kalvi 11th Physics Solutions Chapter 3 Laws of Motion

(d) Force on book m1

  • Downward gravitational force exerted by earth (m1g)
  • Downward force exerted by m2 (N2)
  • Upward force exerted by the table (Ntable)
    Samacheer Kalvi 11th Physics Solutions Chapter 3 Laws of Motion

Question 5.
A bob attached to the string oscillates back and forth. Resolve the forces acting on the bob in to components. What is the acceleration experienced by the bob at an angle θ.
Answer:
The gravitational force (mg) acting downward can be resolved into two components as mg cos θ and mg sin θ
T – tension exerted by the string.
Tangential force FT = maT = mg sin θ
∴ Tangential acceleration aT = g sin θ
Centripetal force Fc = mac = T – mg cos θ
ac = \(\frac { T – mg cos θ }{ m }\)
Samacheer Kalvi 11th Physics Solutions Chapter 3 Laws of Motion

Question 6.
Two masses m1 and m2 are connected with a string passing over a friction-less pulley fixed at the comer of the table as shown in the figure. The coefficient of static friction of mass m1 with the table is µs Calculate the minimum mass m3 that may be placed on m1to prevent it from sliding. Check if m1 = 15 kg, m2 = 10 kg, m3 = 25 and µs = 0.2.
Samacheer Kalvi 11th Physics Solutions Chapter 3 Laws of Motion
Solution:
Let m3 is the mass added on m1
Maximal static friction
\(f_{s}^{\max }\) = µsN = µs (m1 + m3 )g
Here
N = (m1 + m3 )g
Tension acting on string = T = m2 g
Equate (1) and (2)
µs(m1 + m3) = m2g
µsm1 + µsm3 = m2
m3 = \(f_{s}^{\max }\) – m1

(ii) Given,
m1 = 15 kg, m2 = 10 kg : m3 = 25 kg and µs = 0.2
m3 = \(f_{s}^{\max }\) – m1
m3 = \(\frac {10}{ 0.2 }\) – 15 = 50 – 15 = 35 kg
The minimum mass m3 = 35 kg has to be placed on ml to prevent it from sliding. But here m3 = 25 kg only.
The combined masses (m1 + m3) will slide.

Question 7.
Calculate the acceleration of the bicycle of mass 25 kg as shown in Figures 1 and 2.
Samacheer Kalvi 11th Physics Solutions Chapter 3 Laws of Motion
Answer:
Given:
Mass of bicycle m = 25 kg
Fig. I:
Net force acting in the forward direction, F = 500 – 400 = 100 N
acceleration a = \(\frac { F}{ m }\) = \(\frac { 100 }{25}\) = 4 ms-2

Fig. II:
Net force acting on bicycle F = 400 – 400 = 0
∴ acceleration a = \(\frac { F}{ m }\) = \(\frac { 0}{25}\) = 0

SamacheerKalvi.Guru

Question 8.
Apply Lami’s theorem on sling shot and calculate the tension in each string?
Samacheer Kalvi 11th Physics Solutions Chapter 3 Laws of Motion
Answer:
Given F = 50 N, θ = 30°
Here T is resolved into its components as T sin θ and T cos θ as shown.
According to Lami’s theorem,
\(\frac { F}{sin θ}\) = \(\frac { T}{sin (180 – θ)}\) = \(\frac { T}{sin (180 – θ)}\)
\(\frac { F}{sin θ}\) = \(\frac { T}{sin θ}\)
\(\frac { F}{2 sin θ cos θ}\) = \(\frac { T}{sin θ}\) [T = \(\frac { T}{2 cos θ}\) ]
T = \(\frac {T}{2 cos θ}\) = \(\frac { 50}{ 2 cos 30}\) = 28.868 N

Question 9.
A football player kicks a 0.8 kg ball and imparts it a velocity 12 ms-1. The contact between the foot and ball is only for one – sixtieth of a second. Find the average kicking force.
Answer:
Given,
Mass of the ball = 0.8 kg
Final velocity (V) =12 ms-1 and time t =\(\frac {1}{60}\) s
Initial velocity = 0
We know the average kicking force
F = ma = \(\frac {m(v – u)}{t}\) = \(\frac{0.8(12-0)}{\left(\frac{1}{60}\right)}\)
F = 576 N

Question 10.
A stone of mass 2 kg is attached to a string of length 1 meter. The string can withstand maximum tension 200 N. What is the maximum speed that stone can have during the whirling motion?
Solution:
Given,
Mass of a stone = 2 kg,
length of a string = 1 m
Maximum tension = 200 N
The force acting on a stone in the whirling motion is centripetal force. Which is provided by tension of the string.
Tmax = Fmax = \(\frac{m \mathrm{V}_{\mathrm{max}}^{2}}{r}\)
200 = \(v_{\max }^{2}\) = 100
\(v_{\max }^{2}\) = 10 ms-1

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Question 11.
Imagine that the gravitational force between Earth and Moon is provided by an invisible string that exists between the Moon and Earth. What is the tension that exists in this invisible string due’ to Earth’s centripetal force? (Mass of the Moon = 7.34 x 1022 kg, Distance between Moon and Earth = 3.84 x 108 m).

Samacheer Kalvi 11th Physics Solutions Chapter 3 Laws of Motion
Solution:
Given,
Mass of the moon = 7.34 x 1022 kg
Distance between moon and earth = 3.84 x 108 m
Centripetal force = F = \(\frac{m \mathrm{V}^{2}}{r}\) = \(\frac{7.34 \times 10^{22} \times\left(1.023 \times 10^{3}\right)^{2}}{3.84 \times 10^{8}}\) = 2 x 1020

Question 12.
Two bodies of masses 15 kg and 10 kg are connected with light string kept on a smooth surface. A horizontal force F = 500 N is applied to a 15 kg as shown in the figure. Calculate the tension acting in the string.
Samacheer Kalvi 11th Physics Solutions Chapter 3 Laws of Motion
Answer:
Given,
m1  = 15 kg, m2  = 10 kg, F = 500 N
Tension acting in the string T = \(\frac{m_{2}}{m_{1}+m_{2}}\) F
T = \(\frac {10}{25}\) x 500 = 200 N

Question 13.
People often say “For every action there is an equivalent opposite reaction”. Here they meant ‘action of a human’. Is it correct to apply Newton’s third law to human actions? What is meant by ‘action’ in Newton third law? Give your arguments based on Newton’s laws.
Answer:
Newton’s third law is applicable to only human’s physical actions which involves physical force. Third law is not applicable to human’s psychological actions or thoughts.

Question 14.
A car takes a turn with velocity 50 ms-1 on the circular road of radius of curvature To m. Calculate the centrifugal force experienced by a person of mass 60 kg inside the car?
Answer:
Given,
Mass of a person = 60 kg
Velocity of the car = 50 ms-1
Radius of curvature = 10 m
Centrifugal force F = \(\frac{m \mathrm{V}^{2}}{r}\) = \(\frac{60 \times(50)^{2}}{10}\) = 15,000 N

Question 15.
A long stick rests on the surface. A person standing 10 m away from the stick. With what minimum speed an object of mass 0.5 kg should he thrown so that it hits the stick. (Assume the coefficient of kinetic friction is 0.7).
Answer:
Given,
Distance (s) = 10 m
Mass of the object (m) = 0.5 kg
Coefficient of kinetic friction (µ) = 0.7
Work done in moving a body in horizontal surface ω = µR x s = µmg x s
This work done is equal to initial kinetic energy of the object
\(\frac{1}{2} m v^{2}\) = µ mg s
\(\left|v^{2}\right|\) = 2 µgs = 2 x 0.7 x 9.8 x 10
v2 = 14 x 9.8 = 137. 2
v = 11. 71 ms-1

Samacheer Kalvi 11th Physics Laws of Motion Additional Questions Solved

Samacheer Kalvi 11th Physics Laws of Motion Multiple Choice Questions

Question 1.
The concept “force causes motion” was given by –
(a) Galileo
(b) Aristotle
(c) Newton
(d) Joule
Answer:
(b) Aristotle

Question 2.
Who decoupled the motion and force?
(a) Galileo
(b) Aristotle
(c) Newton
(d) Joule
Answer:
(a) Galileo

Question 3.
The inability of objects to move on its own or change its state of motion is called as –
(a) force
(b) momentum
(c) inertia
(d) impulse
Answer:
(c) inertia

Question 4.
Inertia means –
(a) inability
(b) resistance to change its state
(c) movement
(d) inertial frame
Answer:
(b) resistance to change its state

Question 5.
When a bus starts to move from rest, the passengers experience a sudden backward push is an example for –
(a) Inertia of motion
(b) Inertia of direction
(c) Inertia of rest
(d) back pull
Answer:
(c) Inertia of rest

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Question 6.
If the brake is applied in the moving bus suddenly, passengers move forward is an example for –
(a) Inertia of motion
(b) Inertia of direction
(c) Inertia of rest
(d) back pull
Answer:
(a) Inertia of motion

Question 7.
In whirling motion, if the string is cut suddenly, the stone moves tangential to circle is an –
(a) Inertia of motion
(b) Inertia of direction
(c) Inertia of rest
(d) back pull
Answer:
(b) Inertia of direction

Question 8.
Newtons laws are applicable in –
(a) Inertial frame
(b) non inertial frame
(c) in any frame
(d) none
Answer:
(a) Inertial frame

Question 9.
The accelerated train is an example for –
(a) inertial frame
(b) non-inertial frame
(c) both (a) and (b)
(d) none of the above
Answer:
(b) non-inertial frame

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Question 10.
Rate of change of momentum of an object is equal to –
(a) acceleration
(b) work done
(c) force
(d) impulse
Answer:
(c) force

Question 11.
The product of mass and velocity is –
(a) force
(b) impulse
(c) momentum
(d) acceleration
Answer:
(c) momentum

Question 12.
Unit of momentum –
(a) kg ms-2
(b) kg ms-1
(c) MLT-2
(d) MLT-1
Answer:
(b) kg ms-1

Question 13.
According to Newton’s third law –
(a) F12 = F21
(*) F12 = -F21
(c) F12 + F21 = 0
(d) F12 x F21 = 0
Answer:
(a) F12 = F21

Question 14.
According to Newton’s third law –
(a) \(\overrightarrow{\mathrm{F}_{12}}=\overrightarrow{\mathrm{F}_{21}}\)
(b) \(\overrightarrow{\mathrm{F}_{12}}=-\overrightarrow{\mathrm{F}_{21}}\)
(c) \(\mathrm{F}_{12}+\mathrm{F}_{21}\) = 0
(d) \(\mathrm{F}_{12}x\mathrm{F}_{21}\) = 0
Answer:
(b) \(\overrightarrow{\mathrm{F}_{12}}=-\overrightarrow{\mathrm{F}_{21}}\)

Question 15.
The law which is valid in both inertial and non-inertial frame is –
(a) Newton’s first law
(b) Newton’s second law
(c) Newton’s third law
(d) none
Answer:
(c) Newton’s third law

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Question 16.
When a force is applied on a body, it can change –
(a) velocity
(b) momentum
(c) direction of motion
(d) all the above
Answer:
(d) all the above

Question 17.
The rate of change of velocity is 1 ms-2 when a force is applied on the body of mass 75 gm the force is –
(a) 75 N
(b) 0.75 N
(c) 0.075 N
(d) 0.75 x 10-3 N
Answer:
(c) Force is given by
F = m a
= 75 gm x 1 cm s-2 = 75 x 10-3 x 1 = 75 x 10-3 = 0.075 N

Question 18.
The action and reaction forces acting on –
(a) same body
(b) different bodies
(c) either same or different bodies
(d) none of the above
Answer:
(b) different bodies

Question 19.
Newton’s first law of motion gives the concept of –
(a) velocity
(b) energy
(c) momentum
(d) Inertia
Answer:
(d) Inertia

Question 20.
Inertia of a body has direct dependence on –
(a) velocity
(b) area
(c) mass
(d) volume
Answer:
(c) mass

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Question 21.
If a car and a scooter have the same momentum, then which one is having greater speed?
(a) scooter
(b) car
(c) both have same velocity
(d) data insufficient
Answer:
(a) scooter

Question 22.
Newton’s second law gives –
(a) \(\overrightarrow{\mathrm{F}} \propto \frac{d \overrightarrow{\mathrm{P}}}{\mathrm{dt}}\)
(b) \(\overrightarrow{\mathrm{F}}=\frac{d \overrightarrow{\mathrm{P}}}{\mathrm{dt}}\)
(c) \(\overrightarrow{\mathrm{F}}=m \vec{a}\)
(d) all the above
Answer:
(d) all the above

Question 23.
1 dyne is –
(a) 105N
(b) 10-5N
(c) 1N
(d) 10-3N
Answer:
(b) 10-5N

Question 24.
If same force is acting on two masses m1 and m2, and the accelerations of two bodies are a1 and a2 respectively, then –
(a) \(\frac{a_{2}}{a_{1}}=\frac{m_{2}}{m_{1}}\)
(b) \(\frac{a_{1}}{a_{2}}=\frac{m_{1}}{m_{2}}\)
(c) \(\frac{a_{1}}{a_{2}}=\frac{m_{2}}{m_{1}}\)
(d) m1 a1 + m2a2 = 0
Answer:
(c) \(\frac{a_{1}}{a_{2}}=\frac{m_{2}}{m_{1}}\)

Question 25.
If a force \(\overline{\mathrm{F}}\) = 3\(\hat{i}\) – 4\(\hat{j}\) N produces an acceleration of 10 ms-2 on a body, then the mass of a body is –
(a) 10 kg
(b) 9 kg
(c) 0.9 kg
(d) 0.5 kg
Answer:
\(\overline{\mathrm{F}}\) = 3\(\hat{i}\) – 4\(\hat{j}\)
Magnitude:
|\(\overline{\mathrm{F}}\)| = \(\sqrt{9+16}\) = \(\sqrt{25}\) = 5N
F = ma
⇒ m = \(\frac{|\mathrm{F}|}{a}\) = \(\frac{5}{10}\) = \(\frac{1}{2}\) = 0.5 kg

Question 26.
A constant retarding force of 50 N is applied to a body of mass 20 kg moving initially with a speed of 15 ms-1. How long does the body take to stop?
(a) 0.75 s
(b) 1.33 s
(c) 6 s
(d) 35 s
Answer:
Acceleration a = \(\frac{-F}{m}\) = \(\frac{50}{20}\) = – 2.5 ms-2
u = l5 ms-1
v = 0
t = ?
v = u + at
0 = 15 – 2.5t
t = \(\frac{15}{2.5}\) = 6s

Question 27.
Rain drops come down with –
(a) zero acceleration and non zero velocity
(b) zero velocity with non zero acceleration
(c) zero acceleration and non zero net force
(d) none
Answer:
(a) zero acceleration and non zero velocity

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Question 28.
If force is the cause then the effect is –
(a) mass
(b) potential energy
(c) acceleration
(d) Inertia
Answer:
(c) acceleration

Question 29.
In free body diagram, the object is represented by a –
(a) line
(b) arrow
(c) circle
(d) point
Answer:
(d) point

Question 30.
When an object of mass m slides on a friction less surface inclined at an angle 0, then normal force exerted by the surface is –
(a) g cos θ
(b) mg cos θ
(c) g sin θ
(d) mg tan θ
Answer:
(b) mg cos θ

Question 31.
The acceleration of the sliding object in an inclined plane –
(a) g cos θ
(b) mg cos θ
(c) g sin θ
(d) mg sin θ
Answer:
(c) g sin θ

Question 32.
The speed of an object sliding in an inclined plane at the bottom is –
(a) mg cos θ
(b) \(\sqrt{2 s g sin θ}\)
(c) \(\sqrt{2 s g cos θ}\)
(d) \(\sqrt{2 s g tan θ}\)
Answer:
(b) \(\sqrt{2 s g sin θ}\)

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Question 33.
The acceleration of two bodies of mass m1 and m2 in contact on a horizontal surface is –
(a) \(a=\frac{\mathbf{F}}{m_{1}}\)
(b) \(a=\frac{F}{m_{2}}\)
(c)  \(a=\frac{\mathrm{F}}{m_{1}+m_{2}}\)
(d) \(a=\frac{\mathrm{F}}{m_{1} m_{2}}\)
Answer:
(c)  \(a=\frac{\mathrm{F}}{m_{1}+m_{2}}\)

Question 34.
Two blocks of masses m1 and m2 (m1 > m2) in contact with each other on frictionless, horizontal surface. If a horizontal force F is given on m1, set into motion with acceleration a, then reaction force on mass m1 by m2, is –
(a) \(\frac{\mathrm{F} m_{1}}{m_{1}+m_{2}}\)
(b) \(\frac{m_{1} m_{2}}{\mathrm{F} m_{1}}\)
(c) \(\frac{m_{1} m_{2}}{\mathrm{F} m_{2}}\)
(d) \(\frac{\mathrm{F} m_{2}}{m_{1}+m_{2}}\)
Answer:
(d) \(\frac{\mathrm{F} m_{2}}{m_{1}+m_{2}}\)

Question 35.
If two masses m1 and m2 (m1 > m2) tied to string moving over a frictionless pulley, then acceleration of masses –
(a) \(\frac{\left(m_{1}-m_{2}\right)}{m_{1}+m_{2}}\) g
(b) \(\frac{m_{1}+m_{2}}{\left(m_{1}-m_{2}\right)}\) g
(c) \(\frac{2 m_{1} m_{2}}{m_{1}+m_{2}}\) g
(d) \(\frac{m_{1} m_{2}}{2 m_{1} m_{2}}\) g
Answer:
(a) \(\frac{\left(m_{1}-m_{2}\right)}{m_{1}+m_{2}}\) g

Question 36.
if two masses m1 and m2 (m1 > m2)tied to string moving over a frictionless pulley, then acceleration of masses –
(a) \(\frac{\left(m_{1}-m_{2}\right)}{m_{1}+m_{2}}\) g
(b) \(\frac{m_{1}+m_{2}}{\left(m_{1}-m_{2}\right)}\) g
(c) \(\frac{2 m_{1} m_{2}}{m_{1}+m_{2}}\) g
(d) \(\frac{m_{1} m_{2}}{2 m_{1} m_{2}}\) g
Answer:
(a) \(\frac{\left(m_{1}-m_{2}\right)}{m_{1}+m_{2}}\) g

Question 37.
Three massses is in contact as shown. If force F is applied to mass m1, the acceleration of three masses is –
(a) \(\frac{\mathrm{F}}{m_{1}+m_{2}+m_{3}}\)
(b) \(\frac{m_{1} F}{\left(m_{1}+m_{2}+m_{3}\right)}\)
(c) \(\frac{\left(m_{2}+m_{3}\right) F}{\left(m_{1}+m_{2}+m_{3}\right)}\)
(d) \(\frac{m_{3} \mathrm{F}}{m_{1}+m_{2}+m_{3}}\)
Samacheer Kalvi 11th Physics Solutions Chapter 3 Laws of Motion q37
Answer:
(a) \(\frac{\mathrm{F}}{m_{1}+m_{2}+m_{3}}\)

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Question 38.
Three masses in contact is as shown above. If force F is applied to mass m1 then the contact force acting on mass m2 is –
(a) \(\frac{\mathrm{F}}{m_{1}+m_{2}+m_{3}}\)
(b) \(\frac{m_{1} F}{\left(m_{1}+m_{2}+m_{3}\right)}\)
(c) \(\frac{\left(m_{2}+m_{3}\right) F}{\left(m_{1}+m_{2}+m_{3}\right)}\)
(d) \(\frac{m_{3} \mathrm{F}}{m_{1}+m_{2}+m_{3}}\)
Answer:
(c) \(\frac{\left(m_{2}+m_{3}\right) F}{\left(m_{1}+m_{2}+m_{3}\right)}\)

Question 39.
Three masses is contact as shown. It force F is applied to mass m1, then the contact force acting on mass m3 is –
(a) \(\frac{\mathrm{F}}{m_{1}+m_{2}+m_{3}}\)
(b) \(\frac{m_{1} F}{\left(m_{1}+m_{2}+m_{3}\right)}\)
(c) \(\frac{\left(m_{2}+m_{3}\right) F}{\left(m_{1}+m_{2}+m_{3}\right)}\)
(d) \(\frac{m_{3} \mathrm{F}}{m_{1}+m_{2}+m_{3}}\)
Answer:
(d) \(\frac{m_{3} \mathrm{F}}{m_{1}+m_{2}+m_{3}}\)

Question 40.
Two masses connected with a string. When a force F is applied on mass m2. The acceleration produced is –
Samacheer Kalvi 11th Physics Solutions Chapter 3 Laws of Motion q40
(a) \(\frac{\mathrm{F}}{m_{1}+m_{2}}\)
(b) \(\frac{\mathbf{F}}{m_{1}-m_{2}}\)
(c) \(\frac{m_{1}+m_{2}}{\mathrm{F}}\)
(d) \(\frac{m_{3} \mathrm{F}}{m_{1}+m_{2}+m_{3}}\)
Answer:
(a) \(\frac{\mathrm{F}}{m_{1}+m_{2}}\)

Question 41.
Two masses connected with a string. When a force F is applied on mass m2. The force acting on m1 is –
(a) \(\frac{m_{1} \mathrm{F}}{m_{1}+m_{2}}\)
(b) \(\frac{m_{2} \mathrm{F}}{m_{1}+m_{2}}\)
(c) \(\frac{m_{1}+m_{2}}{m_{1}} \mathbf{F}\)
(d) \(\frac{m_{1}+m_{2}}{m_{2}} \mathbf{F}\)
Answer:
(b) \(\frac{m_{2} \mathrm{F}}{m_{1}+m_{2}}\)

Question 42.
If a block of mass m lying on a frictionless inclined plane of length L height h and angle of inclination θ, then the velocity at its bottom is –
(a) g sin θ
(b) g cos θ
(c) \(\sqrt{2 g h}\)
(d) \(\sqrt{2 a sin θ}\)
Answer:
(c) \(\sqrt{2 g h}\)

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Question 43.
If a block of mass m lying on a frictionless inclined plane of length L, height h and angle of inclination θ, then the time take taken to reach the bottom is –
(a) g sing θ
(b) sin θ \(\sqrt{\frac{2 h}{g}}\)
(c) sin θ \(\sqrt{\frac{g}{h}}\)
(d) \(\frac{1}{\sin \theta} \sqrt{\frac{2 h}{g}}\)
Answer:
(d) \(\frac{1}{\sin \theta} \sqrt{\frac{2 h}{g}}\)

Question 44.
A rocket works on the principle of conservation of –
(a) energy
(b) mass
(c) angular momentum
(d) linear momentum
Answer:
(b) mass

Question 45.
A bomb at rest explodes. The total momentum of all its fragments is –
(a) zero
(b) infinity
(c) always 1
(d) always greater then 1
Answer:
(a) zero

Question 46.
A block of mass m1 is pulled along a horizontal friction-less surface by a rope of mass m2 If a force F is given at its free end. The net force acting on the block is –
(a) \(\frac{m_{1} \mathrm{F}}{m_{1}-m_{2}}\)
(b) F
(c) \(\frac{m_{2} \mathrm{F}}{\left(m_{1}+m_{2}\right)}\)
(d) \(\frac{m_{1} \mathrm{F}}{\left(m_{1}+m_{2}\right)}\)
Answer:
(b) F

Question 47.
A block of mass m is pulled along a horizontal surface by a rope. The tension in the rope will be same at all the points –
(a) if the rope is accelerated
(b) if the rope is mass less
(c) always
(d) none of the above
Answer:
(b) if the rope is mass less

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Question 48.
The lines of forces act at a common point is called as –
(a) concurrent forces
(b) co-planar forces
(c) equilibrium
(d) resultant
Answer:
(a) concurrent forces

Question 49.
If the lines of forces act in the same plane, they can be –
(a) concurrent forces
(b) coplanar forces
(c) either concurrent force or coplanar forces
(d) Lami’s force
Answer:
(d) concurrent forces

Question 50.
Lami’s theorem is applicable only when the system of forces are is –
(a) same plane
(b) different plane
(c) equilibrium
(d) none of the above
Answer:
(c) equilibrium

Question 51.
Due to the action of internal forces of the system, the total linear momentum of the system is –
(a) a variable
(b) a constant
(c) always zero
(d) always infinity
Answer:
(c) always zero

Question 52.
The velocity with which a gun suddenly moves backward after firing is –
(a) linear velocity
(b) positive velocity
(c) recoil velocity
(d) v1 + v2
Answer:
(c) recoil velocity

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Question 53.
If a very large force acts on an object for a very short duration, then the force is called as –
(a) Newtonian force
(b) impulsive force
(c) concurrent force
(d) coplanar force
Answer:
(A) impulsive force

Question 54.
The unit of impulse is –
(a) Nm
(b) Ns
(c) Nm2
(d) Ns-2
Answer:
(b) Ns

Question 55.
The force which always opposes the relative motion between an object and the surface where it is placed is –
(a) concurrent force
(b) frictional force
(c) impulsive force
(d) coplanar force
Answer:
(b) frictional force

Question 56.
The force which opposes the initiation of motion of an object on the surface is –
(a) static friction
(b) kinetic friction
(c) friction
(d) zero
Answer:
(d) static friction

Question 57.
When the object is at rest, the resultant of gravitational force and upward normal force is –
(a) Static force
(b) zero
(c) one
(d) infinity
Answer:
(b) zero

Question 58.
The magnitude of static frictional force d lies between –
(a) 0 ≤ f ≤ µsN
(b) 0 ≥f ≥ µsN
(c) 0 and 1
(d) 0 and minimal static frictional force.
Answer:
(a) 0 ≤ f ≤ µsN

Question 59.
The unit of co-efficient of static friction is –
(a) N
(b) N m
(c) N s
(d) no unit
Answer:
(d) no unit

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Question 60.
If the object is at rest and no external force is applied on the object, the static friction acting on the object is –
(a) µsN
(b) zero
(c) one
(d) infinity
Answer:
(d) no unit

Question 61.
When object begins to slide, the static friction acting on the object attains –
(a) zero
(b) minimum
(c) maximum
(d) infinity
Answer:
(c) maximum

Question 62.
The static friction does not depend upon –
(a) the area of contact
(b) normal force
(c) the magnitude of applied force
(d) none of the above
Answer:
(a) the area of contact

Question 63.
Which of the following pairs of materials has minimum amount of coefficient of static friction is –
(a) Glass and glass
(b) wood and wood
(c) ice and ice
(d) steel and steel
Answer:
(c) ice and ice

Question 64.
Kinetic friction is also called as –
(a) sliding friction
(b) dynamic friction
(c) both (a) and (b)
(d) static friction
Answer:
(c) both (a) and (b)

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Question 65.
The unit of coefficient of kinetic friction is/has –
(a) Nm
(b) Ns
(c) Nm2
(d) no unit
Answer:
(d) no unit

Question 66.
The nature of materials in mutual contact decides –
(a) µs
(b) µk
(c) µs or µk
(d) none
Answer:
(c) µs or µk

Question 67.
Coefficient of kinetic friction is less than –
(a) O
(b) one
(c) µs
(d) µsN
Answer:
(c) µs

Question 68.
The static friction –
(a) increases linearly
(b) is constant
(c) zero
(d) varies parabolically
Answer:
(a) increases linearly

Question 69.
The kinetic friction –
(a) increases linearly
(b) is constant
(c) zero
(d) varies parabolically
Answer:
(b) is constant

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Question 70.
Kinetic friction is independent of –
(a) nature of materials
(b) temperature of the surface
(c) applied force
(d) none of the above
Answer:
(c) applied force

Question 71.
The angle between the normal force and the resultant force of normal force and maximum frictional force is –
(a) angle of friction
(b) angle of repose
(c) angle of inclination
(d) none of the above
Answer:
(a) angle of friction

Question 72.
The angle friction θ is given by –
(a) tan µs
(b) tan-1 µs
(c) \(\frac{f S^{\mathrm{max}}}{N}\)
(d) sin-1 µs
Answer:
(b) tan-1 µs

Question 73.
The angle of inclined plane with the horizontal such that an object placed on it begins to slide is –
(a) angle of friction
(b) angle of repose
(c) angle of response
(d) angle of retardation
Answer:
(b) angle of repose

Question 74.
Comparatively, which of the following has lesser value than others?
(a) static friction
(b) kinetic friction
(c) Rolling friction
(d) skiping friction
Answer:
(c) Rolling friction

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Question 75.
The origin of friction is –
(a) electrostatic interaction
(b) electromagnetic interaction magnetic
(c) photon interaction
(d) interaction
Answer:
(b) electromagnetic interaction

Question 76.
Friction can be reduced by –
(a) polishing
(b) lubricating
(c) using ball bearings
(d) all the above
Answer:
(c) using ball bearings

Question 77.
For a particle revolving in a circular path, the acceleration of the particle is –
(a) along the tangent
(b) along the radius
(c) along the circumference of the circle
(d) zero
Answer:
(b) along the radius

Question 78.
A particle moves along a circular path under the action of a force. The work done by the force is –
(a) Positive and non zero
(b) zero
(c) Negative and non zero
(d) none of the above
Answer:
(b) zero

Question 79.
A bullet hits and gets embedded in a solid block resting on a horizontal frictionless table. Which of the following is conserved?
(a) Momentum and kinetic energy
(b) kinetic energy alone
(c) Momentum alone
(d) potential energy alone
Answer:
(c) Momentum alone

Question 80.
The origin of the centripetal force can be –
(a) gravitational force
(b) frictional force
(c) coulomb force
(d) all the above
Answer:
(d) all the above

Question 81.
Centripetal acceleration is –
(a) \(\frac{m v^{2}}{r}\)
(b) \(\frac{v^{2}}{r}\)
(c) r v2
(d) rω
Answer:
(b) \(\frac{v^{2}}{r}\)

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Question 82.
Centripetal acceleration is –
(a) \(\frac{m v^{2}}{r}\)
(b) r ω2
(c) rv2
(d) rω
Answer:
(c) rω2

Question 83.
The centripetal force is –
(a) \(\frac{m v^{2}}{r}\)
(b) rω2
(c) both (a) and (b)
(d) none
Answer:
(c) both (a) and (b)

Question 84.
When a car is moving on a circular track the centripetal force is due to –
(a) gravitational force
(b) frictional force
(c) magnetic force
(d) elastic force
Answer:
(b) frictional force

Question 85.
If the road is horizontal then the normal force and gravitational force are –
(a) equal and along the same direction
(b) equal and opposite
(c) unequal and along the same direction
(d) unequal and opposite
Answer:
(b) equal and opposite

Question 86.
The velocity of a car for safe turn on leveled circular road –
(a) \(v \leq \sqrt{\mu_{s} r g}\)
(b) \(v \geq \sqrt{\mu_{s} r g}\)
(c) \(v=\sqrt{\mu_{s} rg}\)
(d) \(v \leq \mu_{s} rg\)
Answer:
(a) \(v \leq \sqrt{\mu_{s} r g}\)

Question 87.
In a leveled circular road, skidding mainly depends on –
(a) µs
(b) µk
(c) acceleration
(d) none
Answer:
(a) µs

Question 88.
The speed of a car to move on the banked road so that it will have safe turn is –
(a) µsrg
(b) \(\sqrt{r g \tan \theta}\)
(c) rg tan θ
(d) r2g tan θ
Answer:
(b) \(\sqrt{r g \tan \theta}\)

Question 89.
Centrifugal force is a –
(a) pseudo force
(b) real force
(c) forced acting towards center
(d) none of the above
Answer:
(a) pseudo force

Question 90.
Origin of centrifugal force is due to –
(a) interaction between two
(b) inertia
(c) electromagnetic interaction
(d) inertial frame
Answer:
(b) inertia

Question 91.
Centripetal force acts in –
(a) inertial frame
(b) non inertial frame
(c) both (a) and (h)
(d) linear motion
Answer:
(c) both (a) and (b)

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Question 92.
Centrifugal force acts in –
(a) inertial frame
(b) non inertial frame
(c) both (a) and (b)
(d) linear motion
Answer:
(b) non inertial frame

Question 93.
A cricket ball of mass loo g moving with a velocity of 20 ms-1 is brought to rest by a player in 0.05s the impulse of the ball is –
(a) 5 Ns
(b) – 2 Ns
(c) – 2.5 Ns
(d) zero
Answer:
(b) – 2 Ns
mass = 0.1 kg
Initial velocity t = 20 ms-1
Final velocity y = 0
Change in momentum in impulse = m(v – u) = 0.1(0 – 20) = – 2 Ns

Question 94.
If a stone tied at the one end of a string of length 0.5 m is whirled in a horizontal circle with a constant speed 6 ms-1  then the acceleration of the shone is –
(a) 12 ms-2
(b) 36 ms-2
(c) 2π2 ms-2
(d) 72 ms-2
Answer:
(d) Centripetal acceleration = \(\frac{v^{2}}{r}\) = \(\frac{6^{2}}{0.5}\) = \(\frac{36}{0.5}\) = 72 ms-2

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Question 95.
A block of mass 3 kg is at rest on a rough inclined plane with angle of inclination 30° with horizontal. If .is 0.7, then the frictional force is –
(a) 17.82 N
(b) 1.81 N
(c) 3.63 N
(d) 2.1 N
Answer:
(a) Frictional force = µmg cos θ = 0.7 x 3 x 9.8 cos 30° = 17.82 N

Question 96.
Two masses 2 kg and 4 kg are tied at the ends of a mass less string and which is passing over a friction-less pulley. The tension in the string is –
(a) 3.68 N
(b) 78.4 N
(c) 26 N
(d) 13.26 N
Answer:
(c) Tension in the string T = \(\frac{2 m_{1} m_{2}}{\left(m_{1}+m_{2}\right)}\)g
T = \(\frac{2 x 2 x 4}{2 + 4}\) x 9.8 = \(\frac{16}{6}\) x 9.8 = 26.13 N

Question 97.
A bomb of 10 kg at rest explodes into two pieces of mass 4 kg and 6 kg. if the velocity of 4 kg mass is 6 ms-1 then the velocity of 6 kg is –
(a) – 4 ms-1
(b) – 6 ms-1
(c) – 24 ms-1
(d) – 2.2 ms-1
Answer:
(a) According to law of conservation of momentum
m1v1 + m2v2 = 0
v2 = –\(\frac{m_{1} v_{1}}{m_{2}}\) = \(\frac{4 x 6}{6}\) = -4ms-1

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Question 98.
A body is subjected under three concurrent forces and it is in equilibrium. The resultant of any two forces is –
(a) coplanar with the third force
(b) is equal and opposite to third force
(c) both (a) and (b)
(d) none of the above
Answer:
(c) both (a) and (b)

Question 99.
An impulse is applied to a moving object with the force at an angle of 20° with respect to velocity vector. The angle between the impulse vector and the change in momentum vector is –
(a) 0°
(b) 30°
(c) 60°
(d) 120°
Answer:
(a) Impulse and change in momentum are in same direction. So the angle is zero.

Question 100.
A bullet of mass m and velocity v1 is fired into a large block of wood of mass M. The final velocity of the system is-
(a) \(\frac{v_{1}}{m+\mathrm{M}}\)
(b) \(\frac{m v_{1}}{m+\mathrm{M}}\)
(c) \(\frac{m+m}{m} v_{1}\)
(d) \(\frac{m+m}{m-M} v_{1}\)
Answer:
(b) \(\frac{m v_{1}}{m+\mathrm{M}}\)

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Question 101.
A block of mass 2 kg is placed on the floor. The co – efficient of static friction is 0.4. The force of friction between the block and floor is –
(a) 2.8 N
(b) 7.8 N
(c) 2 N
(d) zero
Answer:
(b) The force required to move = = µR = µmg = 0.4 x 2 x 9.8 = 7.84 N

Question 102.
A truck weighing 1000 kg is moving with velocity of 50 km/h on smooth horizontal roads. A mass of 250 kg is dropped into it. The velocity with which it moves now is –
(a) 12.5 km/h
(b) 20 km/h
(c) 40 km/h
(d) 50 km/h
Answer:
(c) According to law of conservation of linear momentum
m2 v2 = (m1 + m2)v2
v2 = \(\frac{m_{1} v_{1}}{m_{1}+m_{2}}\) = \(\frac{1000 \times 50}{1250}\) = 40 km/h

Question 103.
A body of mass loo g is sliding from an inclined plane of inclination 30°. if u = 1.7, then the frictional force experienced is –
(a) \(\frac{3.4}{\sqrt{3}}\)N
(b) 1.47 N
(c) \(\frac{\sqrt{3}}{3.4}\)N
(d) 1.38 N
Answer:
(b) Frictional force F = µ mg cos θ = 1.7 x 0.1 x 10 cos 30°= \(\frac{1.7}{2}\) x \(\sqrt{3}\) = 1.47 N

Samacheer Kalvi 11th Physics Laws of Motion Short Answer Questions (1 Mark)

Question 1.
A passenger sitting in a car at rest, pushes the car from within. The car doesn’t move, why?
Answer:
For motion, there should be external force.

Question 2.
Give the magnitude and directions of the net force acting on a rain drop falling with a constant speed.
Answer:
as \(\overline{\mathrm{a}}\) = 0 so \(\overline{\mathrm{F}}\) = 0.

Question 3.
Why the passengers in a moving car are thrown outwards when it suddenly takes a turn?
Answer:
Due to inertia of direction.

Question 4.
You accelerate your car forward. What is the direction of the frictional force on a package resting on the floor of the car?
Answer:
The package in the accelerated car (a non inertial frame) experiences a Pseudo force in a direction opposite to that of the motion of the car. The frictional force on the package which acts opposite to this pseudo force is thus in the same direction (forward) as that of the car.

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Question 5.
What is the purpose of using shockers in a car?
Answer:
To decrease the impact of force by increasing the time for which force acts.

Question 6.
Why are types made of rubber not of steel?
Answer:
Since coefficient of friction between rubber and road is less than the coefficient of friction between steel and road.

Question 7.
Wheels are made circular. Why?
Answer:
Rolling friction is less than sliding friction.

Question 8.
If a ball is thrown up in a moving train, it comes back to the thrower’s hands. Why?
Answer:
Both during its upward and downward motion, the ball continues to move inertia of motion with the same horizontal velocity as the train. In this period, the ball covers the same horizontal distance as the train and so it comes back to the thrower’s hand.

Question 9.
Calculate the force acting on a body which changes the momentum of the body at the rate of 1 kg-m/s2 .
Answer:
As F = rate change of momentum
F = 1 kg-m/s2 = 1N

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Question 10.
On a rainy day skidding takes place along a curved path. Why?
Answer:
As the friction between the types and road reduces on a rainy day.

Question 11.
Why does a gun recoils when a bullet is being fired?
Answer:
To conserve momentum.

Question 12.
Why is it difficult to catch a cricket ball than a tennis ball even when both are moving with the same velocity?
Answer:
Being heavier, cricket ball has higher rate of change of momentum during motion so more force sumed.

Question 13.
The distance travelled by a moving body is directly proportional to time. Is any external force acting on it?
Answer:
As s ∝ t, so acceleration a = 0, therefore, no external force is acting on the body.

Question 14.
Calculate the impulse necessary to stop a 1500 kg car moving at a speed of 25 ms-1.
Answer:
Use formula I = change in momentum = m(v – u) (Impulse – 37500 Ns)

Question 15.
Lubricants are used between the two parts of a machine. Why?
Answer:
To reduce friction and so to reduce wear and tear.

Question 16.
What provides the centripetal force to a car taking a turn on a level road?
Answer:
Force of friction between the type and road provides centripetal force.

Question 17.
A body is acted upon by a number of external forces. Can it remain at rest?
Answer:
Yes, if the external forces acting on the body can be represented in magnitude and direction by the sides of a closed polygon taken in the same order.

Question 18.
Bodies of larger mass need greater initial effort to put them in motion. Why?
Answer:
As F = ma so for given a, more force will be required to put a large mass in motion.

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Question 19.
An athlete runs a certain distance before taking a long jump Why?
Answer:
So that inertia of motion may help him in his muscular efforts to take a longer jump.

Question 20.
Action and reaction forces do not balance each other. Why?
Answer:
As they acts on different bodies.

Question 21.
The wheels of vehicles are provided with mudguards. Why?
Answer:
When the wheel rotates at a high speed, the mud sticking to the wheel flies off tangentially, this is due to inertia of direction. If order that the flying mud does not spoil the clothes of passer by the wheels are provided with mudguards.

Question 22.
China wares are wrapped in straw paper before packing. Why?
Answer:
The straw paper between the China ware increases the Time of experiencing the jerk during transportation. Hence impact of force reduces on China wares.

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Question 23.
Why is it difficult to walk on a sand?
Answer:
Less reaction force.

Question 24.
The outer edge of a curved road is generally raised over the inner edge Why?
Answer:
In addition to the frictional force, a component of reaction force also provides centripetal force.

Question 25.
Explain why the water doesn’t fall even at the top of the circle when the bucket full of water is upside down rotating in a vertical circle?
Answer:
Weight of the water and bucket is used up in providing the necessary centripetal force at the top of the circle.

Question 26.
Why does a speedy motor cyclist bends towards the center of a circular path while taking a turn on it?
Answer:
So that in addition of the frictional force, the horizontal component of the normal reaction also provides the necessary centripetal forces.

Question 27.
An impulse is applied to a moving object with a force at an angle of 20° wr.t. velocity vector, what is the angle between the impulse vector and change in momentum vector ?
Answer:
Impulse and change in momentum are along the same direction. Therefore angle between these two vectors is zero.

Samacheer Kalvi 11th Physics Laws of Motion Short Answer Questions (2 Marks)

Question 28.
A man getting out of a moving bus runs in the same direction for a certain distance. Comment.
Answer:
Due to inertia of motion.

Question 29.
If the net force acting upon the particle is zero, show that its linear momentum remains constant.
Answer:
As F x \(\frac {dp}{dt}\)
when F = 0, \(\frac {dp}{dt}\) = 0 so P = constant

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Question 30.
A force of 36 dynes is inclined to the horizontal at an angle of 60°. Find the acceleration in a mass of 18 g that moves in a horizontal direction.
Answer:
F = 36 dyne at an angle of 60°
Fx = F cos 60° = 18 dyne
Fx = max
So ax = \(\frac{F_{x}}{m}\) = 1 cm /s2

Question 31.
The motion of a particle of mass m is described by h = ut + \(\frac {1}{2}\) gt2. Find the force acting on particle.
Answer:
a = ut + \(\frac {1}{2}\) gt2
find a by differentiating h twice w.r.t.
a = g
As F = ma so F = mg (answer)

Question 32.
A particle of mass 0.3 kg is subjected to a force of F = -kx with k= 15 Nmr-1. What will be its initial acceleration if it is released from a point 20 cm away from the origin?
Answer:
As F = ma so F = -kx = ma
a = \(\frac {-kx}{m}\)
for x = 20 cm, ⇒ a = -10 m/s2.

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Question 33.
A 50 g bullet is fired from a 10 kg gun with a speed of 500 ms-1. What is the speed of the recoil of the gun?
Answer:
Initial momentum = 0
Using conservation of linear momentum mv + MV = 0
V = \(\frac {-mv}{M}\) ⇒ V = 2.5 m/s

Question 34.
Smooth block is released at rest on a 45° incline and then slides a distance d. If the time taken of slide on rough incline is n times as large as that to slide than on a smooth incline. Show that coefficient of friction, µ = \(\left(1-\frac{1}{n^{2}}\right)\)
Answer:
When there is no friction, the block slides down the inclined plane with acceleration. a = g sin θ
when there is friction, the downward acceleration of the block is a’ = g (sin θ – µ cos θ)
As the block Slides a distance d in each case so
d = \(\frac {1}{2}\) at2 = \(\frac {1}{2}\) a’t’2
\(\frac{a}{a^{\prime}}=\frac{t^{\prime 2}}{t^{2}}=\frac{(n t)^{2}}{t^{2}}\) = n2
or \(\frac {g sin θ}{g(sin θ – µ cos θ)}\) = n2
Solving, we get (Using θ = 45°)
µ = 1 – \(\frac{1}{n^{2}}\)

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Question 35.
A spring balance is attached to the ceiling of a lift. When the lift is at rest spring balance reads 49 N of a body hang on it. If the lift moves:

  1. Downward
  2. upward, with an acceleration of 5 ms2
  3. with a constant velocity.

What will be the reading of the balance in each case?
Answer:
1.  R = m(g – a) = 49 N
so = m = \(\frac {49}{9.8}\) = 5 kg
R = 5 (9.8 – 5)
R = 24 N

2. R = m(g + a)
R = 5 (9.8 + 5)
R = 74 N

3.  as a = 0 so R = mg = 49 N

Question 36.
A bob of mass 0.1 kg hung from the ceiling of room by a string 2 m long is oscillating. At its mean position the speed of a bob is 1 ms-1. What is the trajectory of the ‘oscillating bob if the string is cut when the bob is –

  1. At the mean position
  2. At its extreme position.

Answer:

  1. Parabolic
  2. vertically downwards

Question 37.
A block placed on a rough horizontal surface is pulled by a horizontal force F. Let f be the force applied by the rough surface on the block. Plot a graph of f versus F.
Answer:

Samacheer Kalvi 11th Physics Solutions Chapter 3 Laws of Motion
Unto point A, f = F (50 Long as block is stationary) beyond A, when F increases, block starts moving f remains constant.

Question 38.
A mass of 2 kg is suspended with thread AB. Thread CD of the same type is attached to the other end of 2 kg mass.

  • Lower end of the lower thread is pulled gradually, hander and hander is the downward direction so as to apply force on AB Which of the thread will break & why?
  • If the lower thread is pulled with a jerk, what happens?

Answer:

  • Thread AB breaks down
  • CD will break.

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Question 39.
A block of mass M is held against a rough vertical wall by pressing it with a finger. If the coefficient of friction between the block and the wall is p and the acceleration due to gravity is g, calculate the minimum force required to be applied by the finger to held the block against the wall?
Answer:
Samacheer Kalvi 11th Physics Solutions Chapter 3 Laws of Motion
For the block not to fall f = Mg
But f = µR = µF so
µF = Mg
F = \(\frac {Mg}{µ}\)

Samacheer Kalvi 11th Physics Laws of Motion Short Answer Questions (3 Marks) & Numericals

Question 40.
A block of mass 500 g is at rest on a horizontal table. What steady force is required to give the block a velocity of 200 cm s-2 in 4 s?
Answer:
Use F – ma
a = \(\frac {v – u}{ t }\) = \(\frac {200- 0}{ 4 }\) = 50 cm/s2
F = 500 x 50 = 25,000 dyne.

Question 41.
A force of 98 N is just required to move a mass of 45 kg on a rough horizontal surface. Find the coefficient of friction and angle of friction?
Answer:
F = 48 N,R = 45 x 9.8 = 441 N
µ = \(\frac {F’}{ R}\) = 0.22
Angle of friction θ = tan-1 0.22 = 12°24′

Question 42.
Calculate the force required to move a train of 2000 quintal up on an incline plane of 1 in 50 with an acceleration of 2 ms-2. The force of friction per quintal is 0.5 N.
Answer:
Force of friction = 0.5 N per quintal
f = 0.5 x 2000 = 1000 N
m = 2000 quintals = 2000 x 100 kg
sin θ = \(\frac {1}{50}\), a – 2 m/s2
In moving up an inclined plane, force required against gravity
mg sin θ = 39200 N
And force required to produce acceleration = ma
= 2000 x 100 x 2 = 40,0000 N
Total force required = 1000 + 39,200 + 40,0000 = 440200 N.

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Question 43.
A force of 100 N gives a mass m1, an acceleration of 10 ms-2 and of 20 ms-2 to a mass m2.
What acceleration must be given to it if both the masses are tied together?
Answer:
Suppose, a = acceleration produced if m1 and m2 are tied together,
F = 100 N
Let a1 and a2 be the acceleration produced in m1 and m2 respectively.
∴ a1 and a2 = 20ms-2 (given)
Again m1 = \(\frac{\mathrm{F}}{a_{1}}\) and m2 = \(\frac{\mathrm{F}}{a_{2}}\)
⇒ m1 = \(\frac {100}{10}\) = 10kg
and m2 = \(\frac {100}{20}\) = 5kg
∴ m1 + m2 = 10 + 5 = 15
so, a = \(\frac{\mathbf{F}}{m_{1}+m_{2}}\) = \(\frac {100}{15}\) = \(\frac {20}{3}\) = 6.67 ms2

Question 44.
The pulley arrangement of figure are identical. The mass of the rope is negligible. In (a) mass m is lifted up by attaching a mass (2m) to the other end of the rope. In (b), m is lifted up by pulling the other end of the rope with a constant downward force F = 2 mg. In which case, the acceleration of m is more?
Samacheer Kalvi 11th Physics Solutions Chapter 3 Laws of Motion
Answer:
Case (a):
a = \(\frac {2m – m}{2m + m}\) g = a = \(\frac {g}{3}\)
Case (b):
FBD of mass m
ma’ = T – mg
ma’ = 2 mg – mg
⇒ ma’ = mg
a’ = g
So in case (b) acceleration of m is more.

Question 45.
Figure shows the position-time graph of a particle of mass 4 kg. What is the
Samacheer Kalvi 11th Physics Solutions Chapter 3 Laws of Motion
(a) Force on the particle for t < 0, t > 4s, 0 < t < 4s?
(b) Impulse at t = 0 and t = 4s?
(Consider one dimensional motion only)
Answer:
(a) For t < 0. No force as Particles is at rest. For t > 4s, No force again particle comes at rest.
For 0 < t < 4s, as slope of OA is constant so velocity constant i.e., a = 0, so force must be zero.

(b) Impulse at t = 0
Impulse = change in momentum
I = m(v – w) = 4(0 – 0.75) = 3 kg ms-1
Impulse at t = 4s
1 = m(v – u) = 4 (0 – 0.75) = -3 kg ms-1

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Question 46.
What is the acceleration of the block and trolley system as the figure, if the coefficient of kinetic friction between the trolley and the surface is 0.04? Also Calculate friction in the string: Take g = 10 m/s2, mass of the string is negligible.
Samacheer Kalvi 11th Physics Solutions Chapter 3 Laws of Motion
Answer:
Free body diagram of the block
30 – T = 3a
Free body diagram of the trolley
Samacheer Kalvi 11th Physics Solutions Chapter 3 Laws of Motion
T – fk = 20 a ………….(2)
where fk = µk= 0.04 x 20 x 10 = 8 N
Solving (i) & (ii), a = 0.96 m/s2 and T = 27.2 N

Question 47.
Three blocks of masses ml = 10 kg, m2 = 20 kg are connected by strings on smooth horizontal surface and pulled by a force of 60 N. Find the acceleration of the system and frictions in the string.
Samacheer Kalvi 11th Physics Solutions Chapter 3 Laws of Motion
Solution:
All the blocks more with common acceleration a under the force F = 60 N.
F = (m1 + m2 + m3)a
a = \(\frac{\mathrm{F}}{\left(m_{1}+m_{2}+m_{3}\right)}\) = 1 m/s2
to determine, T1 →Free body diagram of m1.
Samacheer Kalvi 11th Physics Solutions Chapter 3 Laws of Motion
T1 = m1a = 10 x 1 = 10 N
to determine, T2 →Free body diagram of m3
Samacheer Kalvi 11th Physics Solutions Chapter 3 Laws of Motion
F – T2 = m3a
Solving, we get T2 = 30 N

SamacheerKalvi.Guru

Question 48.
The rear side of a truck is open and a box of 40 kg mass is placed 5m away from the open end. The coefficient of friction between the box and the surface below it is 0.15 on a straight road, the truck starts from rest and accelerates with 2 m/s2. At what distance from the starting point does the box fall off the truck ? (ignore the size of the box)
Answer:
Force on the box due to accelerated motion of the truck
F = ma = 40 x 2 = 80 N (in forward direction)
Reaction on the box, F’ = F = 80 N (in backward direction)
Force of limiting friction, f = µR = 0 .15 x 40 x 10 = 60 N
Net force on the box in backward direction is P = F’ f = 80 – 60 = 20 N
Backward acceleration in the box = a= \(\frac {p}{m}\) = \(\frac {20}{40}\) = 0.5 ms-2
t = time taken by the box to travel s = 5 m and falls off the truck, then from
s = ut + \(\frac {1}{2}\) at2
5 = 0 x t + \(\frac {1}{2}\) x 0.5 x t2
t = 4.47
If the truck travels a distance x during this time
then x = 0 x 4.34 +\(\frac {1}{2}\) x 2 x (4.471)2
x = 19.98 m

Question 49.
A block slides down as incline of 30° with the horizontal. Starting from rest, it covers 8 m in the first 2 seconds. Find the coefficient of static friction.
Use s = ut + \(\frac {1}{2}\) at2
a = \(\frac{2 s}{t^{2}}\) at2 as u = 0
µ = \(\frac{g sin θ – a}{g Cos θ }\)
Putting the value and solving, µ = 0.11

Question 50.
A helicopter of mass 2000 kg rises with a vertical acceleration of 15 m/s2 . The total mass of the crew and passengers is 500 kg. Give the magnitude and direction of the:
(a) Force on the floor of the helicopter by the crew and passenger.
(b) Action of the rotor of the helicopter on the surrounding air
(c) Force on the helicopter due to the surrounding air (g = 10 m/s2 )
Answer:
(a) Force on the floor of the helicopter by the crew and passengers
= apparent weight of crew and passengers
= 500(10+ 15)
=12500 N

(b) Action of rotor of helicopter on surrounding air is Obviously vertically downwards, because helicopter rises on account of reaction of this force. Thus force of action
= (2000 + 500) (10 + 15)
= 2500 x 25
= 62,500 N

(c) Force on the helicopter due to surrounding air is obviously a reaction. As action and reaction are equal and opposite, therefore
Force of reaction F’ = 62,500 vertically upwards.

SamacheerKalvi.Guru

Question 51.
A rectangular box lies on a rough inclined surface. The coefficient of friction between the surface and the box is (µ). Let the mass of the box be m.

  1.  At what angle of inclination θ of the plane to the horizontal will the box just start to slide down the plane ?
  2. What is the force acting on the box down the plane, if the angle of inclination of the plane is increased to a > θ.
  3. What is the force needed to be applied upwards along the plane to make the box either remain stationary or just move up with uniform speed ?
  4. What is the force needed to be applied upwards along the plane to pk kg f make the box move up the plane with acceleration a ?

Answer:
1. When the box just starts sliding
µ = tanθ
or 0 = tan-1 µ

2. Force acting on the box down the plane
= mg (sin a – µ cos a)

3. Force needed mg (sin a + µ cos a)

4. Force needed = mg (sin a + µ cos a) + ma.
Samacheer Kalvi 11th Physics Solutions Chapter 3 Laws of Motion

Question 52.
Two masses of 5 kg and 3 kg are suspended with help of mass less in extensible string as shown. Calculate T1 and T2 when system is going upwards with acceleration m/s2. (Use g 9.8 m/s2)
Answer:
According Newton’s second law of motion
(1) T1 – (m1 + m2)g = (m1 + m2)a
T1 = (m1 + m2)(a + g) = (5 + 3) (2 + 9.8)
T1 = 94.4 N

(2) T2 – m2g = m2a
T2 = m2 (a + g)
T2 = 3(2 + 9.8)
T2 = 35.4 N

Samacheer Kalvi 11th Physics Solutions Chapter 3 Laws of Motion

Question 53.
There are few forces acting at a Point P produced by strings as shown, which is at rest. Find the forces F1 & F1
Samacheer Kalvi 11th Physics Solutions Chapter 3 Laws of Motion
Answer:
Using Resolution of forces IN and 2N and then applying laws of vector addition. Calculate for F1 & F1.
F1 = \(\frac{1}{\sqrt{2}}\) N, F2 = \(\frac{3}{\sqrt{2}}\)N

Question 54.
A hunter has a machine gun that can fire 50g bullets with a velocity of 150 ms A 60 kg tiger springs at him with a velocity of 10 ms-1. How many bullets must the hunter fire into the target so as to stop him in his track?
Answer:
Given m = mass of bullet = 50 gm = 0.50 kg
M = mass of tiger = 60 kg
v = Velocity of bullet – 150 m/s
V = Velocity of tiger = – 10 m/s
(v It is coming from opposite direction n = no. of bullets fired per second at the tiger so as to stop it.)
Pi = 0, before firing ……..(i)
Pf = n (mv) + MV …………(ii)
∴ From the law of conservation of momentum,
Pi = Pf
⇒ 0 = n (mv) + MV
n = \(\frac{MV}{mv}\) = \(\frac{-60 \times(-10)}{0.05 \times 150}\) = 80

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Question 55.
Two blocks of mass 2 kg and 5 kg are connected by an ideal string passing over a pulley. The block of mass 2 kg is free to slide on a surface inclined at an angle of 30° with the horizontal whereas 5 kg block hangs freely. Find the acceleration of the system and the tension in the string.
Samacheer Kalvi 11th Physics Solutions Chapter 3 Laws of Motion
Let a be the acceleration of the system and T be the Tension in the string. Equations of motions for 5 kg and 2 kg blocks are
5g – T = 5a
T – 2g sin θ – f = 2a
where f = force of limiting friction
= µR = µ mg cos θ = 0.3 x 2 g x cos 30°
Solving (1) & (2)
a = 4.87 m/s2

Samacheer Kalvi 11th Physics Solutions Chapter 3 Laws of Motion Read More »

Samacheer Kalvi 11th Maths Solutions Chapter 2 Basic Algebra Ex 2.4

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Tamilnadu Samacheer Kalvi 11th Maths Solutions Chapter 2 Basic Algebra Ex 2.4

Question 1.
Construct a quadratic equation with roots 7 and -3.
Solution:
Let the given roots be α = 7 and β = -3
Sum of the roots α + β = 7 + (-3)
α + β = 7 – 3 = 4
Product of the roots αβ = (7)(-3)
αβ = -21
The required quadratic equation is
x2 – (sum of two roots) x + Product of the roots = 0
x2 – 4x – 21 = 0

Question 2.
A quadratic polynomial has one of its zeros 1 + \(\sqrt{5}\) and it satisfies p(1) = 2. Find the quadratic polynomial.
Solution:
Given α = 1 + \(\sqrt{5}\) So, β = 1 – \(\sqrt{5}\)
Samacheer Kalvi 11th Maths Solutions Chapter 2 Basic Algebra Ex 2.4 1
The quadratic polynomial is
p(x) = x2 – (α + β)x + αβ
p(x) = k (x2 – 2x – 4)
p( 1) = k(1 – 2 – 4) = -5 k
Given p (1) = 2
Samacheer Kalvi 11th Maths Solutions Chapter 2 Basic Algebra Ex 2.4 2

The Polynomial Roots Calculator will find the roots of any polynomial with just one click.

Samacheer Kalvi 11th Maths Solutions Chapter 2 Basic Algebra Ex 2.4

Question 3.
If α and β are the roots of the quadratic equation x2 + \(\sqrt{2}\)x + 3 = 0, form a quadratic polynomial with zeroes 1/α, 1/β.
Solution:
α and β are the roots of the equation x2 + \(\sqrt{2}\)x + 3 = 0
Samacheer Kalvi 11th Maths Solutions Chapter 2 Basic Algebra Ex 2.4 3
Samacheer Kalvi 11th Maths Solutions Chapter 2 Basic Algebra Ex 2.4 4

Samacheer Kalvi 11th Maths Solutions Chapter 2 Basic Algebra Ex 2.4

Question 4.
If one root of k(x – 1)2 = 5x – 7 is double the other root, show that k = 2 or – 25.
Solution:
k(x – 1)2 = 5x – 7
(i.e.,) k(x2 – 2x + 1) – 5x + 7 = 0
x2 (k) + x(-2k – 5) + k + 1 = 0
kx2 – x(2k + 5) + (k + 7) = 0
Here it is given that one root is double the other.
So let the roots to α and 2α
Samacheer Kalvi 11th Maths Solutions Chapter 2 Basic Algebra Ex 2.4 5
2(4k2 + 25 + 20k) = 9k (k + 7)
2(4k2 + 25 + 20k) = 9k2 + 63k
8k2 + 50 + 40k – 9k2 – 63k = 0
-k2 – 23k + 50 = 0
k2 + 23k – 5o = 0
(k + 25)(k – 2) = 0
k = -25 or 2

Question 5.
If the difference of the roots of the equation 2x2 – (a + 1)x + a – 1 = 0 is equal to their product then prove that a = 2.
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 2 Basic Algebra Ex 2.4 6

Samacheer Kalvi 11th Maths Solutions Chapter 2 Basic Algebra Ex 2.4

Question 6.
Find the condition that one of the roots of ax2 + bx + c may be
(i) negative of the other
(ii) thrice the other
(iii) reciprocal of the other.
Solution:
(i) Let the roots be α and -β
Sum of the roots = – b/a = 0 ⇒ b = 0

(ii) Let the roots be α, 3α
Samacheer Kalvi 11th Maths Solutions Chapter 2 Basic Algebra Ex 2.4 7

Question 7.
If the equations x2 – ax + b = 0 and x2 – ex + f = 0 have one root in common and if the second equation has equal roots that ae = 2(b + f).
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 2 Basic Algebra Ex 2.4 8

Samacheer Kalvi 11th Maths Solutions Chapter 2 Basic Algebra Ex 2.4

Question 8.
Discuss the nature of roots of
(i) -x2 + 3x + 1 = 0
(ii) 4x2 – x – 2 = 0
(iii) 9x2 + 5x = 0
Solution:
(i) -x2 + 3x + 1 = 0
x2 – 3x – 1 = 0 ———- (1)
Compare this equation with the equation
ax2 + bx + c = 0 ——– (2)
we have a = 1, b = -3, c = -1
Discriminant = b2 – 4ac
b2 – 4ac = (-3)2 – 4 × 1 × – 1
= 9 + 4 =13
b2 – 4ac = 13 > 0
∴ The two roots are real and distinct.

(ii) 4x2 – x – 2 = 0
4x2 – x – 2 = 0 ——(3)
Compare this equation with the equation
ax2 + bx + c = 0 (4)
we have a = 4 , b = – 1, c = – 2
Discriminant = b2 – 4ac
b2 – 4ac = (-1)2 – 4 (4) (-2)
= 1 + 32
= 33
b2 – 4ac = 33 >0
∴ The two roots are real and distinct.

(iii) 9x2 + 5x = 0
9x2 + 5x = 0 ——- (5)
Compare this equation with the equation
ax2 + bx + c = 0 ——– (6)
we have a = 9, b = 5 , c = 0
Discriminant = b2 – 4ac
b2 – 4ac = 52 – 4 × 9 × 0
b2 – 4ac = 25 > 0
∴ The two roots are real and distinct.

Question 9.
Without sketching the graphs find whether the graphs of the following functions will intersect the x- axis and if so in how many points.
(i) y = x2 + x + 2
(ii) y = x2 – 3x – 1
(iii) y = x2 + 6x + 9
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 2 Basic Algebra Ex 2.4 20
Samacheer Kalvi 11th Maths Solutions Chapter 2 Basic Algebra Ex 2.4 21

Samacheer Kalvi 11th Maths Solutions Chapter 2 Basic Algebra Ex 2.4

Completing the Square Calculator is a free online tool that displays the variable value for the quadratic equation using completing the square method.

Question 10.
Write f(x) = x2 + 5x + 4 in completed square form.
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 2 Basic Algebra Ex 2.4 22

Samacheer Kalvi 11th Maths Solutions Chapter 2 Basic Algebra Ex 2.4 Additional Questions

Question 1.
Find the values of k so that the equation x2 = 2x (1 + 3k) + 7(3 + 2k) = 0 has real and equal roots.
Solution:
The equation is x2 – x(2) (1 + 3k) + 7 (3 + 2k) = 0
The roots are real and equal
⇒ ∆ = 0 (i.e.,) b2 – 4ac = 0
Here a = 1, b = -2 (1 + 3k), c = 7(3 + 2k)
So b2 – 4ac = 0
⇒ [-2 (1 + 3k)]2 – 4(1) (7) (3 + 2k) = 0
(i.e.,) 4 (1 + 3k)2 – 28 (3 + 2k) = 0
(÷ by 4) (1 + 3k)2 – 7(3 + 2k) = 0
1 + 9k2 + 6k – 21 – 14k = 0
9k2 – 8k – 20 = 0
(k – 2)(9k + 10) = 0
Samacheer Kalvi 11th Maths Solutions Chapter 2 Basic Algebra Ex 2.4 23
To solve the quadratic inequalities ax2 + bx + c < 0 (or) ax2 + bx + c > 0

Samacheer Kalvi 11th Maths Solutions Chapter 2 Basic Algebra Ex 2.4

Question 2.
If the sum and product of the roots of the quadratic equation ax2 – 5x + c = 0 are both equal to 10 then find the values of a and c.
Solution:
The given equation is ax2 – 5x + c = 0
Let the roots be α and β Given α + β = 10 and αβ = 10
Samacheer Kalvi 11th Maths Solutions Chapter 2 Basic Algebra Ex 2.4 24

Question 3.
If α and β are the roots of the equation 3x2 – 4x + 1 = 0, form the equation whose roots are \(\frac{\alpha^{2}}{\beta}\) and \(\frac{\beta^{2}}{\alpha}\)
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 2 Basic Algebra Ex 2.4 25
Samacheer Kalvi 11th Maths Solutions Chapter 2 Basic Algebra Ex 2.4 26

Samacheer Kalvi 11th Maths Solutions Chapter 2 Basic Algebra Ex 2.4

Question 4.
If one root of the equation 3x2 + kx – 81 = 0 is the square of the other then find k.
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 2 Basic Algebra Ex 2.4 27

Question 5.
If one root of the equation 2x2 – ax + 64 = 0 is twice that of the other then find the value of a.
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 2 Basic Algebra Ex 2.4 28

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