Q 11-05-026JEE MainEAMCET 2011 (Engineering)Hard
A ball is let fall from a height $h_0$. It makes $n$ collisions with the horizontal ground. If after $n$ collisions it rebounds with a velocity $v_n$ and the ball rises to a height $h_n$, then the coefficient of restitution for the collision is
Answer: (A) $e = \left(\dfrac{h_n}{h_0}\right)^{\frac{1}{2n}}$
Each bounce multiplies the speed by $e$, and height $\propto$ speed$^2$, so each bounce multiplies the height by $e^2$:
$$h_n = e^{2n}h_0 \;\Rightarrow\; e = \left(\frac{h_n}{h_0}\right)^{\frac{1}{2n}}$$
Solution by Sreeraj P, M.Sc Physics