Question

If the momentum of a body is increased $n$ times, its kinetic energy increases-

• A. $n$ times
• B. $2n$ times
• C. $\sqrt{n}$ times
• D. $n^2$ times

Answer 1

The correct option is D $n^2$ times

It is known that $P=mv$ and $E=\frac{1}{2}m{v}^2$

$E=\frac{P^2}{2m}\therefore E\propto P^2$

i.e. if $P$ is increased $n$ times then $E$ will increase $n^2$ times.