Question

A hollow sphere of mass $m$ = 1 kg and radius $R$ = 1 m 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 $v$ = 2 m/s partially penetrates the left side of the sphere. The velocity of the sphere just after collision with bullet is:

• A. 1 m/s
• B. 0.5 m/s
• C. 1.5 m/s
• D. 2 m/s

Answer 1

The correct option is A

1 m/s

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 $v^{\prime }$ be the velocity of bullet and sphere just after the collision.

From conservation of momentum

$(m+m)v^{\prime }=mv$
or $v^{\prime }=\frac{v}{2}=1m/sec$