Question

A ball is dropped from a height h above floor. If the coefficient of restitution between the floor and the ball is 'e' , the ball, after the first rebound, will rise to a height of

• A. $eh$
• B. $e^{2}h$
• C. $\frac{h}{e}$
• D. $\frac{h}{e^2}$

Answer 1

The correct option is B

$e^{2}h$

If $u$ is the speed of the ball with which it strikes the floor and $u^{\prime }$ its speed after rebound, then the coefficient of restitution between the floor and the ball is defined as the ratio $e=\frac{u^{\prime }}{u}$. Thus, the speed after rebound is u' = eu.
Now, $u=\sqrt{2gh}$
and $u^{\prime }=\sqrt{2g{h}^{\prime }}$
where h' is the height to which the ball rises after rebound.
Therefore, $\frac{u}{u^{\prime }}=\sqrt{\frac{h}{h^{\prime }}}$
or $h^{\prime }={\left(\frac{u^{\prime }}{u}\right)}^{2}h=e^{2}h$
Hence, the correct choice is (b).