A hollow sphere of mass m = 1 kg and radius R = 1m rests on a smooth horizontal surface. A simple pendulum having a string of length R and bob of mass m = 1 kg hangs from the topmost point of the sphere as shown in the figure. A bullet of mass m = 1 kg and velocity v = 2m/sec hits the sphere as shown in the figure and sticks to it. The velocity of the sphere just after the collision with the bullet is:
A hollow sphere of mass m = 1 kg and radius R = 1m rests on a smooth horizontal surface. A simple pendulum having a string of length R and bob of mass m = 1 kg hangs from the topmost point of the sphere as shown in the figure. A bullet of mass m = 1 kg and velocity v = 2m/sec hits the sphere as shown in the figure and sticks to it. The velocity of the sphere just after the collision with the bullet is:
The correct option is A 1 m/sec
During the collision, the pendulum and the ball will exert forces on each other only along the string. Since the string is vertical, the net momentum of ball and particle along horizontal direction will remain conserved.Let v’ be the velocity of bullet and sphere just after the collision.
From conservation of momentum
(m+m)v′=mv or v′=v/2=1m/sec
1 m/sec
During the collision, the pendulum and the ball will exert forces on each other only along the string. Since the string is vertical, the net momentum of ball and particle along horizontal direction will remain conserved.Let v’ be the velocity of bullet and sphere just after the collision.
From conservation of momentum
(m+m)v′=mv or v′=v/2=1m/sec
