Question

A stone is dropped from a height $h$. It hits the ground with a certain momentum $p$. If the same stone is dropped from a height $100 \%$ more than the previous height, the momentum when it hits the ground will change by -

• A. 41 %
• B. 200 %
• C. 100%
• D. 60%

Answer 1

Answer: (A)

When a stone is dropped from a height $h$, it hits the ground with a momentum
$P=m \sqrt{2 g h}\,\,\,$...(i)
where $m$ is the mass of the stone.
When the same stone is dropped from a height $2 h$
(i.e. $100 \%$ of initial), then its momentum with which it hits the ground becomes
$P^{\prime}=m \sqrt{2 g(2 h)}=\sqrt{2} P \text { (Using (i)) ...(ii) }$
$\%$ change in momentum $=\frac{P^{\prime}-P}{P} \times 100 \%$
$=\frac{\sqrt{2} P-P}{P} \times 100 \%=41 \%$