Question

Two bodies $A$ and $B$ having masses in the ratio of $3:1$ possess the same kinetic energy. The ratio of linear momentum of $B$ to $A$ is :

• A. $1:3$
• B. $3:1$
• C. $1:\sqrt{3}$
• D. $\sqrt{3}:1$

Answer 1

Answer: (C)

$1:\sqrt{3}$

Kinetic energy and momentum are related as

$KE=\frac{P^2}{2m}$

$\frac{K_a}{K_b}=\frac{P_a^2}{P_b^2}.\frac{m_b}{m_a}$

$1=\frac{P_a^2}{P_b^2}.\frac{m_b}{m_a}$[since KE is same]

$\frac{P_b}{P_a}=\sqrt{\frac{m_b}{m_a}}=\sqrt{\frac{1}{3}}$

Option C.