Question

A rubber ball is dropped from a height of $5m$ on a planet, where the acceleration due to gravity is not known. On bouncing it rises to $1.8m$. 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 $\frac{2}{5}$

Initial height $h_i=5m$

Final height after collision $h_f=1.8$

Using $h_f=e^2{h}_i$

Or $1.8=e^2\times 5$

$⟹e=0.6$

Let the initial velocity of the ball just before collision be $V$.

Velocity of ball just after collision $V_f=eV=-0.6V$

Factor by which the velocity is lost $=\frac{V-0.6V}{V}=0.4=\frac{2}{5}$