A light rigid rod has a small ball of mass m attached to its one end. The other end is hinged on a table and the rod can rotate freely in vertical plane. The rod is released from vertical position and while falling the ball at its end strikes a hemisphere of mass m lying freely on the table. The collision between the ball and the hemisphere is elastic. The radius of hemisphere and length of the rod are R and 2R respectively. Find the velocity of the hemisphere after collision.

Answer

`(4 sin theta sqrt(gR(1-sin theta)))/(1+sin^(2) theta)` where `sin theta = (1)/(sqrt(5))`