Question

The bodies of masses 2m and m have their kinetic energies in the ratio 8 : 1. Then the ratio of their momentum is:

• A. 1:1
• B. 2:1
• C. 4:1
• D. 8:1

Answer 1

The correct option is C 4:1

The relation between kinetic energy $\left(K\right)$ and momentum $\left(p\right)$ is given by, $K=\frac{p^2}{2m}$ where $m$ be the mass of the body

So, $p=\sqrt{2mK}$

Hence, $\frac{p_1}{p_2}=\frac{\sqrt{2\left(2m\right)K_1}}{\sqrt{2m{K}_2}}=\sqrt{2\left(8/1\right)}=\frac{4}{1}$