Question

A body is allowed to fall freely under gravity from a height of $10\, m$. 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 $h=10\, m$. Potential energy at this height $=$ $m g h .$ On reaching the ground, $K E=m g h .$ Since the body loses $25 \%$ of energy due to impact, kinetic energy of the body after one impact $=0.75 \,mgh$. If $v_{1}$ is the initial upward velocity after the impact, we have
$\frac{1}{2} m v_{1}^{2}=0.75 mgh =\frac{3}{4} mgh \text { or } v_{1}^{2}=1.5\, g h$
The height $h_{1}$ to which the body will rise is
$h_{1}=\frac{v_{1}^{2}}{2\, g}=\frac{1.5 \,g h}{2\, g}$
$=0.75 h=0.75 \times 10=7.5\, m (\because h=10 m )$