[UPSC CSE 1998] Conservation Laws (Q48, 20M)

A smooth sphere A of mass m and speed u impinges obliquely on a sphere B of mass (M>m) at rest. The velocity of A before collision makes an angle \theta with the line of centres at the time of impact. Show that A is deflected through a right angle if \tan^2\theta=e\frac{M-m}{M+m} where e is the coefficient of restitution.