A heavy ball of radius R is travelling on a smooth horizontal surface with a velocity of u0 towards left. A horizontally moving small ball of mass m strikes it at a height `(R)/(2)` above the centre while travelling with velocity u towards right.
(a) After collision the small ball moves in vertically upwards direction with velocity u. Prove that this can happen only if `u gt sqrt(3)u_(0)`
(b) Find the velocity of small ball after collision if the collision is elastic and the balls are smooth.

Answer

(b) `sqrt(u^(2)+3u_(0)^(2)+3u u_(0))`