Question

Two bodies of masses $3\text{kg}$ and $6\text{kg}$ possess kinetic energies of $6\text{J}$ and $10\text{J}$ respectively. What is the ratio of their linear momentum?

• A. $\sqrt{\frac{3}{10}}$
• B. $\sqrt{\frac{3}{5}}$
• C. $\sqrt{\frac{10}{3}}$
• D. $\sqrt{\frac{5}{3}}$

Answer 1

The correct option is A $\sqrt{\frac{3}{10}}$

Let $KE$ be the kinetic energy and $P$ is the linear momentum

The relation between kinetic energy and linear momentum is given by $\because KE=\frac{P^2}{2m}$

So, for body of mass $3\text{kg}$, given $K.E=6\text{J}$
$K{E}_1=\frac{P_1^2}{2m_1}$
$\Rightarrow 6=\frac{P_1^2}{2\times 3}.$
$\Rightarrow P_1=\mathrm{6.....}\left(i\right)$

Similarly for body of mass $6\text{kg}$, given $K.E=10\text{J}$

$10=\frac{P_2^2}{2\times 6}$
$\Rightarrow P_2=\sqrt{120}...\left(ii\right)$

Dividing $\left(i\right)$ by $\left(ii\right)$

$\frac{P_1}{P_2}=\frac{6}{\sqrt{120}}=\sqrt{\frac{3}{10}}$

Hence option $\left(a\right)$ is the correct answer.