Question

Two masses of 1 g and 4 g are moving with equal kinetic energies. The ratio of the magnitudes of their moment is:

• A. 4:1
• B. $\sqrt{2}$:1
• C. 1:2
• D. 1:16

Answer 1

The correct option is C 1:2

Kinetic energy $K=\frac{1}{2}m{v}^2=\frac{1}{2}\frac{m^2{v}^2}{m}=\frac{p^2}{2m}$

Where $p$ is momentum

$\Rightarrow \frac{p_1^2}{2m_1}=\frac{p_2^2}{2m_2}$given

$\Rightarrow \frac{p_1^2}{p_2^2}=\frac{m_1}{m_2}=\frac{1}{4}\Rightarrow \frac{P_1}{P_2}=\frac{1}{2}$