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

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Aicharya · Accepted Answer

A ball dropped from a height $h_{1}$ on reaching the planet's surface will have a velocity given by $v_{1}=\sqrt{2 g h_{1}}$ Let $v_{2}$ be the velocity with which the ball bounces. It will attain a height $h_{2}$ given by $\begin{aligned} v_{2} &= \sqrt{2 g h_{2}} \ \therefore \quad \frac{v_{2}}{v_{1}} &= 0.6 \ \text { or } 1-\frac{v_{2}}{v_{1}} &= 1-0.6 \text { or } \frac{v_{1}-v_{2}}{v_{1}} = 0.4 = \frac{2}{5} \end{aligned}$ Hence the correct choice is (b).

A rubber ball is dropped from a height of \(5 \mathrm{~m}\) on a planet where the acceleration due to…

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