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:
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