A ball is thrown horizontally from a height h above a staircase as shown in the figure. If the coefficient of restitution for any collision between the ball and the staircase is e, then the value of h for which the ball will bounce the same height above each step, is

A

$\frac{4 d}{3}$

B

2d

C

$\frac{3 d}{4}$

D

$\frac{3 d}{2}$

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The correct Answer is:C

Kinetic energy of a body of mass m moving with velocity ${\to v}_{1}$ w.r.t. an observer moving with ${\to v}_{2}$
$K E_{1 / 2} = \frac{m}{2} {| {\to v}_{1} - {\to v}_{2} |}_{1}^{2}$
$\Rightarrow K E_{1 / 2}$ depends on velocity of observer implies statement -2 is false
$K E_{loss} = \frac{1}{2} \frac{m_{1} m_{2}}{m_{1} + m_{2}} {| {\to v}_{1} - {\to v}_{3} |}_{1}^{2}$
where ${\to v}_{1}$ is velocity of first particle & ${\to v}_{3}$ is velocity of other particle & it is independent of velocity of observer.

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Updated on:21/07/2023

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