Question

A body is allowed to fall freely under gravity from a height of $10m$. If it loses $25\%$ of its energy on impact with the ground, to what height will it rise after one impact?

• A. 2.5 m
• B. 5.0 m
• C. 7.5 m
• D. 9.0 m

Answer 1

Answer: (C)

Height $h=10m$. Potential energy at this height $=$ $mgh.$ On reaching the ground, $KE=mgh.$ Since the body loses $25\%$ of energy due to impact, kinetic energy of the body after one impact $=0.75mgh$. If $v_1$ is the initial upward velocity after the impact, we have
$\frac{1}{2}m{v}_1^2=0.75mgh=\frac{3}{4}mgh\text{ or }{v}_1^2=1.5gh$
The height $h_1$ to which the body will rise is
$h_1=\frac{v_1^2}{2g}=\frac{1.5gh}{2g}$
$=0.75h=0.75\times 10=7.5m(\because h=10m)$