Suppose the rod with the balls A and B of the previous problem is clamped at the center in such a way that it can rotate freely about a horizontal axis through the clamp. The system is kept at rest in the horizontal position. A particle P of the same mass m is dropped from a height h on the ball B. The particle collides with B and sticks to it. (a) Find the angular momentum and the angular speed of the system just after the collision. (b) What should be the minimum value of h so that the system makes a full rotation after the collision.
Given:
Mass of particle P = m
Height from which it is dropped = h
Velocity of the particle P before collision with B= 
Consider the bodies of particle P and ball B as a single system
Net external torque acting on the system is zero
after the collision, the angular momentum of the rod
(B) When mass 2m is at top of the rod and mass m is at the bottom, the rod will rotate automatically. The total potential energy will be given as
Therefore,
