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Question 14 Marks

Gas molecules move in random motion inside the container. The pressure exerted by the gas is due to the continuous collision of the molecules against the walls of the container. Due to this continuous collision, the walls experience a continuous force which is equal to the total momentum imparted to the walls per second.

1. If the mass of each molecule is halved and speed is doubled, find the ratio of initial and final pressure:
(a) 1:16 (b) 1:4 (c) 1:8 (d) 1:2
2. The pressure exerted by the gases is:
(a) inversely proportional to the density
(b) inversely proportional to the square of the density
(c) directly proportional to the density
(d) directly proportional to the square of the density
3. If the force of attraction between the molecules suddenly disappears, then what will be the change in pressure:
(a) pressure increase
(b) pressure decrease
(c) pressure remains constant
(d) pressure falls
4. If the pressure of a given gas is halved at a certain temperature. what will be its volume:
(a) becomes triple (b) becomes double (c) remains constant d) becomes half
OR
Dimension formula for R?
(a) $M ^1 L^2 T^2 K^{-1}$
(b) $M ^1 L^1 T^{-1}$
(c) $M ^{-1} L^0 T^1$
(d) $M ^1 L^2 T^{-2} K^{-1}$

Answer

1. (d) $1: 2$
Explanation: 1:2
2. (c) directly proportional to the density
Explanation: directly proportional to the density
3. (a) pressure increase
Explanation: pressure increase
4. (b) becomes double
Explanation: becomes double
OR
(d) $M ^1 L^2 T^{-2} K^{-1}$
Explanation: $M ^1 L^2 T^{-2} K^{-1}$

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Question 24 Marks

Certain collisions are referred to as elastic collisions. Elastic collisions are collisions in which both momentum and kinetic energy are conserved. The total system kinetic energy before the collision equals the total system kinetic energy after the collision. If total kinetic energy is not conserved, then the collision is referred to as an inelastic collision.
The coefficient of restitution, denoted by (e), is the measure of degree elasticity of collision. It is defined as the ratio of the final to inital relative speed between two objects after they collide. It normally ranges from 0 to 1 where 1 would be a perfectly elastic collision. A perfectly inelastic collision has a coefficient of 0 . In real life most of the collisions are neither perfectly elastic nor perfectly inealstic and $0< e <1$.

1. The following are the data of a collision between a truck and a car.
Mass of the car $=1000 kg$
Mass of the truck $=3000 kg$
Mass of the truck Before collision:
Speed of the car $=20 m / s$
Momentum of the car $=20000 kg m / s$
Speed of the truck $=20 m / s$
Momentum of the truck $=60000 kg m / s$
After collision:
Speed of the car $=40 m / s$ in the opposite direction
Momentum of the car $=40000 kg m / s$ in the opposite direction
Speed of the truck $=0$
Momentum of the truck $=0$
The collision is
(a) Both elastic since kinetic energy and momentum is conserved
(b) Elastic since momentum is conserved
(c) Inelastic since kinetic energy is conserved
(d) Elastic since kinetic energy is conserved
2. The coefficient of restitution is the measure of
(a) Malleability of a substance (b) Conductivity of a substance
(c) degree of elasticity of collision (d) Elasticity of a substance
3. Coefficient of restitution is defined as
(a)

(b) Relative velocity after collision x relative velocity before collision
(c) Relative velocity after collision + relative velocity before collision
(d)

OR
In real life most of the collisions are
(a) Range of coefficient of restitution is 0 < e < 1
(b) both neither perfectly nor perfectly inelastic and range of coefficient of restitution is 0 < e < 1.
(c) neither perfectly elastic nor perfectly inelastic
(d) perfectly inelastic
4. For perfectly elastic and perfectly inelastic collision, the value of coefficient of restitution are respectively
(a) $+1,-1$ (b) 0,1 (c) $0,-1$ (d) 1,0

Answer

1. (b) Elastic since momentum is conserved
Explanation: From the given data kinetic energy is 800000 Joules, before and after collision and momentum is $40000 kg m / s$ before and after the collision. So the collision is elastic.
2. (c) degree of elasticity of collision
Explanation: degree of elasticity of collision
3. (d)

Explanation:

OR
(b) both neither perfectly nor perfectly inelastic and range of coefficient of restitution is $0< e <1$.
Explanation: both neither perfectly nor perfectly inelastic and range of coefficient of restitution is $0< e <1$.
4. (d) 1,0
Explanation: 1, 0

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Physics 4 Marks Question

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