A rod AB of mass M and length L is lying on a horizontal frictionless surface. A particle of mass m travelling along the surface hits the end A of the rod with a velocity v 0 in a direction perpendicular to AB . The collision is perfectly elastic and after the collision, the particle comes to rest. The ratio m M is

Step-by-step solution

Using the principle of conservation of linear momentum mv 0 = Mv cm Using the principle of conservation of angular momentum mv 0 L 2 = ML 2 12 ω Since the collision is completely elastic, the velocity of approach is equal to the velocity of separation v 0 = v cm + ω L 2 ⇒ v 0 = m M v 0 + 3 m M v 0 ⇒ m M = 1 4