Question

Two particles have masses $m$ and $4m$ and their kinetic energies are in the ratio $2:1$. What is the ratio of their linear momenta?

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

Answer 1

The correct option is A $\frac{1}{\sqrt{2}}$

As $KE=\frac{p^2}{2m}$
$\therefore \frac{p_1^2}{p_2^2}=\frac{m_1}{m_2}\cdot \frac{{KE}_1}{{KE}_2}=\frac{1}{4}\cdot \frac{2}{1}=\frac{1}{2}$
$\Rightarrow \frac{p_1}{p_2}=\frac{1}{\sqrt{2}}$