(a) Explain the meaning of inertia with the help of an example.

(b) Two balls of same size but of different materials, rubber and iron are kept on the smooth floor of a moving train. The brakes are applied suddenly to stop the train. Will the balls start rolling? If so, in which direction? Will they move with the same speed? Give reasons for your answer.

OR

(a) A ball of mass m is thrown vertically upward from the ground with an initial speed v, its speed decreases continuously till it becomes zero. Thereafter, the ball begins to fall downward and attains the speed v again before striking the ground. It implies that the magnitude of initial and final momentum of the ball are same. Yet, it is not an example of conservation of momentum. Explain why?

(b) A bullet of mass 20 g is horizontally fired with a velocity 150 m s^–1 from a pistol of mass 2 kg. What is the recoil velocity of the pistol?

(a) Inertia is the resistance of the object to any change in its motion, including a change in direction. An object will stay still or keep moving at the same speed and in a straight line, unless it is acted upon by an outside force.

The tendency of an object to resist any change in its state of rest or of uniform motion is called inertia.

Examples-

1. A ball rolling down a hill continues to roll unless frictional force stops it.

2. A person sitting in the bus falls on one side when the bus takes a turn.

3. The swirling of tea continues in the glass even after we stop stirring it.

(b) The balls will be moving in the same direction in which train was moving due to inertia of motion. The train comes to rest due to applied breaks but due to inertia of motion, the balls being to roll forward. Masses of balls are not same therefore different inertial forces are acting on them. Iron ball has more mass hence more inertia than rubber ball of same size. Thus iron ball will attain less speed than rubber ball.

OR

(a) The law of conservation of momentum is applicable only when no external force is applied to the object that is an isolated system. Here in this example when the ball falls down it is due to the gravitational force of earth. This is an external force. Therefore this is not an example of conservation of momentum.

(b) Mass of bullet, m₁ = 20g = 0.02kg

Mass of pistol, m₂ = 2kg

Initial velocity of bullet (u₁) and pistol (u₂) = 0m/s

Final velocity of bullet, v₁ =150m/s

The direction of bullet is taken from left to right, thus positive

Let, V be the recoil velocity of the pistol.

Total momenta of the piston and bullet before the fire, gun at rest = (2+ 0.02)kg × 0 m/s ---(1)

= 0

Total momenta of the piston and bullet after the fire = 0.02kg(150m/s) + 2kg × V

= (3+2V) kg m/s ----------- (2)

Equating equation 1 and 2 according to the law of conservation of momentum, i.e. total momentum after the fire is equal to total momentum before the fire,

3+2V=0

V = -1.5m/s

Negative sign shows the opposite direction of recoil of pistol to the direction of bullet.