By how much does kinetic energy increase if the momentum is increased by 20%

The correct option is 44%.

Let us understand the relationship between kinetic energy and momentum to see why this is the correct answer.

Kinetic energy ($K$) and momentum ($p$) of an object of mass $m$ are related by the formula:
$K=\frac{p^2}{2m}$

Let the initial momentum be $p_1$ and the initial kinetic energy be $K_1=\frac{p_1^2}{2m}$.

According to the problem, the momentum is increased by 20%. Therefore, the new momentum $p_2$ is given by:
$p_2=p_1+0.20p_1=1.2p_1$

Now, let us calculate the new kinetic energy $K_2$ using the new momentum:
$K_2=\frac{p_2^2}{2m}=\frac{{\left(1.2p_1\right)}^2}{2m}=1.44·\frac{p_1^2}{2m}=1.44K_1$

The fractional increase in kinetic energy is:
$\frac{K_2-K_1}{K_1}=\frac{1.44K_1-K_1}{K_1}=0.44$

To express this as a percentage, we multiply by 100%:
Percentage Increase = $0.44\times 100\%=44\%$

Thus, the kinetic energy increases by 44% when momentum is increased by 20%.