Question

If the kinetic energy of a body is increased by $100\%$, then the change in momentum of the body is :

• A. $\text{4.14 \%}$
• B. $\text{41.4 \%}$
• C. $\text{141.4 \%}$
• D. None of these

Answer 1

The correct option is B $\text{41.4 \%}$

We know that,

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

$\Rightarrow p\propto \sqrt{KE}$

So,

$\frac{p_2}{p_1}=\sqrt{\frac{K{E}_2}{K{E}_1}}$

$\Rightarrow \frac{p_2}{p}=\sqrt{\frac{2K}{K}}=1.414$

$\Rightarrow \frac{p_2-p}{p}=0.414$

$\Rightarrow \frac{p_2-p}{p}\%=41.4\%$

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