Question

A rubber ball is dropped from a height of 5 m on a planet where the acceleration due to gravity is not known. On bouncing, it rises to 1.8 m. The ball loses its velocity on bouncing by a factor of

• A. $\frac{16}{25}$
• B. $\frac{2}{5}$
• C. $\frac{3}{5}$
• D. $\frac{9}{25}$

Answer 1

The correct option is B

$\frac{2}{5}$

If ball falls from height $h_1$ and bounces back up to height $h_2$ then $e=\sqrt{\frac{h_2}{h_1}}$

Similarly if the velocity of ball before and after collision are $v_{1}and{v}_2$ respectively then $e=\frac{v_2}{v_1}$

$So\frac{v_2}{v_1}=\sqrt{\frac{h_2}{h_1}}=\sqrt{\frac{1.8}{5}}=\sqrt{\frac{9}{25}}=\frac{3}{5}$

i.e. fractional loss in velocity $=1-\frac{v_2}{v_1}=1-\frac{3}{5}=\frac{2}{5}$