Question

The kinetic energy of a body becomes twice its initial value. The new momentum of the body will be

• A. $2$ times
• B. $\sqrt{2}$ times
• C. $4$ times
• D. unchanged

Answer 1

The correct option is B

$\sqrt{2}$ times

We know that

The kinetic energy in terms of the momentum and mass of the body is,

$$\begin{gathered} \Rightarrow E=\frac{p^2}{2m} \\ \Rightarrow E\propto p^2 \end{gathered}$$

When the energy of the body becomes twice its initial value, let $E_1$ is the initial kinetic energy, and $E_2$ is the final kinetic energy,

$$\begin{gathered} \Rightarrow \frac{E_1}{E_2}=\frac{{p^2}_1}{{p^2}_2} \\ \Rightarrow \frac{1}{2}=\frac{{p^2}_1}{{p^2}_2} \\ \Rightarrow \frac{1}{\sqrt{2}}=\frac{p_1}{p_2} \\ \Rightarrow p_2=\sqrt{2}{p}_1 \end{gathered}$$

Thus, we conclude that if the kinetic energy of a body becomes twice its initial value then the new momentum of the body will be $p_2=\sqrt{2}{p}_1$

Hence, option B is the correct answer.