Question

If the kinetic energy of a body increases by 0.1%, the percent increase of its momentum will be

• A. 0.05%
• B. 0.1%
• C. 1.0%
• D. 10%

Answer 1

The correct option is A

0.05%

Step 1: Given data

The increase in kinetic energy of a body is 0.1%

Step 2: Finding the percentage change in momentum

We know that,

The relation between kinetic energy and momentum of a body is given by

$$\begin{gathered} E_k=\frac{p^2}{2m} \\ {p}^2=2m{E}_k \\ p=\sqrt{2m{E}_k} \\ p\propto \sqrt{E_k} \end{gathered}$$

The percentage increase in its momentum will be,

$$\begin{gathered} \frac{△p}{p}=\frac{1}{2}\frac{△E_k}{E_k} \\ \frac{△p}{p}=\frac{1}{2}\times 0.1\% \\ \frac{△p}{p}=0.05\% \end{gathered}$$

The percentage increase in its momentum is 0.05%

Hence, option (a) is correct.