A body is fired from point P and strikes at Q inside a smooth circular wall (in horizontal plane) as shown in figure. It rebounds to point S (diametrically opposite to P). The coefficient of restitution will be 
     

A body is fired from point P and strikes at Q inside a smooth circular wall (in horizontal plane) as
Let  $v_1$  and $v_2$  be the speed of the body before and after striking Q.
$v_1\sin \alpha =v_2\cos \alpha$ (as there is no friction so component of velocity along the tangential direction remains same) 
$e{v}_1\cos \alpha =v_2\cos (\frac{\pi }{2}-\alpha )$  (from coefficient of restitution equation)
$\Rightarrow e=\frac{v_2\sin \alpha }{v_1\cos \alpha }={\tan }^2\alpha$