Question

Two masses of $M$ and $4M$ are moving with equal kinetic energy. The ratio of their linear momentum is

• A. $1:8$
• B. $1:4$
• C. $1:2$
• D. $4:1$

Answer 1

The correct option is C

$1:2$

Step 1: Given data

The relation between linear momentum and kinetic energy is $p=\sqrt{2mKE}$

where $p$is momentum, $m$ is mass and $KE$ is the kinetic energy

For the masses $M$ and $4M$ we have same kinetic energy

Step 2: Calculation

$$\begin{gathered} \frac{p_1}{p_2}=\frac{\sqrt{2MKE}}{\sqrt{2\left(4M\right)KE}} \\ \Rightarrow \frac{p_1}{p_2}=\frac{\sqrt{1}}{\sqrt{4}} \\ \Rightarrow \frac{p_1}{p_2}=\frac{1}{2} \end{gathered}$$

Therefore, the ratio of their linear momentum will be 1 : 2.

Hence, Option (C) is correct.