First slide

Coefficient of restitution

Question

A ball is dropped from a height of 5 m. If it rebound upto height of 1.8 m, then the ratio of velocities of the ball after and before rebound is :

Moderate

A

$\frac{3}{5}$
B

$\frac{2}{5}$
C

$\frac{1}{5}$
D

$\frac{4}{5}$

Solution

$\begin{array}{l} e = \frac{v_{2}}{v_{1}} = \frac{\sqrt{2 {gh}_{2}}}{\sqrt{2 {gh}_{1}}} = \sqrt{\frac{h_{2}}{h_{1}}} \\ = \sqrt{\frac{1 .8}{5}} = \sqrt{\frac{18}{50}} = \sqrt{\frac{9}{25}} = \frac{3}{5} \end{array}$

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