Question

Two masses of $1g$ and $4g$ are moving with equal kinetic energies. The ratio of the magnitudes of the linear momenta is

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

Answer 1

The correct option is B $1:2$

Given, $m_1=1g$ and $m_2=4g$
And kinetic energy, $K_1=K_2$
Linear momenta is given by,
$p=\sqrt{2mK}$
So, ratio of magnitude of linear momenta,
$\frac{p_1}{p_2}=\frac{\sqrt{2m_1{K}_1}}{\sqrt{2m_2{K}_2}}$
$\frac{p_1}{p_2}=\sqrt{\frac{1}{4}}=\frac{1}{2}$
Final answer: $\left(c\right)$