A ball is let fall from a height $h_0$. It makes n collisions with the earth. After $'n'$ collisions it rebounds with a velocity $;v_n'$ and the ball rises to a height $h_n$ then coefficient of restitution, is given by

Question

$$\begin {array} {1 1} (a)\;e= \bigg[\frac{h_n}{h_0}\bigg]^{1/2n} & \quad (b)\;e= \bigg[\frac{h_0}{h_n}\bigg]^{1/2n} \\ (c)\;e= \frac{1}{n} \sqrt {\frac{h_n}{h_0}} & \quad (d)\;e= \frac{1}{n}\sqrt {\frac{h_0}{h_n}} \end {array}$$