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) $e = \left(\dfrac{h_n}{h_0}\right)^{\frac{1}{2n}}$
Concept. Each bounce multiplies speed by $e$ and height by $e^2$.
Step 1. After $n$ bounces. $h_n = e^{2n}h_0$.
Step 2. Solve. $e = \left(\dfrac{h_n}{h_0}\right)^{1/2n}$.
Answer. $e = \left(\dfrac{h_n}{h_0}\right)^{\frac{1}{2n}}$ (Option A).
Solution by Sreeraj P, M.Sc Physics