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Question

A hollow sphere of mass m = 1 kg and radius R = 1m rests on a smooth horizontal surface. A simple pendulum having string of length R and bob of mass m = 1 kg hangs from top most point of the sphere as shown in the figure. A bullet of mass m = 1 kg and velocity v = 2m/sec partially penetrates the left side of the sphere. The velocity of the sphere just after collision with bullet is:


A

1 m/sec

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B

0.5 m/sec

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C

1.5 m/sec

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D

2 m/sec

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Solution

The correct option is A

1 m/sec


During collision the pendulum does not experience any impulse in the horizontal direction. Hence the

horizontal momentum of bullet + sphere is conserved for the duration of collision. Let v be the velocity

of bullet and sphere just after the collision.

From conservation of momentum

(m + m)v = mv or v = v2 = 1m/sec


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