Q62 / 120 · NEET 2012 (Mains) · Physics
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$68 \%$
- Correct answerB$41 \%$
- C$200 \%$
- D$100 \%$
Solution
Velocity $v=\sqrt{2 g h}$
and momentum $p=m v$
From Eqs. (i) and (ii), we have
Here
$\frac{p_2}{p_1}=\sqrt{\frac{h_2}{h_1}}$
$$
\begin{aligned}
& \therefore \quad \frac{p_2}{p_1}=\sqrt{\frac{2 h}{h}}=\sqrt{2} \\
& p_2=1.414 p_1 \\
& \% \text { change }=\frac{p_2-p_1}{p_1} \times 100=41 \%
\end{aligned}
$$
Hence, the correct answer is option: 'B'.