Question

Two identical bodies are allowed to fall from different heights $h_1$ and $h_2$. The ratio of their momentum when they reach the ground will be

• A. $h_1:h_2$
• B. $h_1^2:h_2^2$
• C. $\sqrt{h_1}:\sqrt{h_2}$
• D. $1$

Answer 1

Answer: (C)

$\sqrt{h_1}:\sqrt{h_2}$

We know,

$P=mv$

$u=0$

$\begin{array}{c}2as=v^2-u^2\\ \sqrt{2a{h}_1}=v\\ 2as=v^2-u^2\\ \sqrt{2a{h}_2}=v\\ \sqrt{\frac{2a{h}_1}{2a{h}_2}}=\frac{\sqrt{h_1}}{\sqrt{h_2}}\end{array}$

$\therefore$ Option $C$ is correct.