A ball of mass M falls from a height h on a floor which coefficient of restitution is e . height att

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5.Work, Energy, Power and Collision

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A ball of mass $M$ falls from a height $h$ on a floor which the coefficient of restitution is $e$. The height attained by the ball after two rebounds is

A

$e^2h$

B

$e{h^2}$

C

$e^4h$

D

$\frac{h}{{{e^4}}}$

Solution

A ball falling from height $h$ reaches the floor with velocity.

$v=\sqrt{2 g h}$

By definition

$\mathrm{e}=\frac{\text { velocity of separation }}{\text { velocity of approach }}$

Rebound velocity $=e \sqrt{2 \mathrm{hg}}$

Rebound height $=e^{2} h$

After two rebounds, height $=\mathrm{e}^{4} \mathrm{h}$

Standard 11

Physics

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