Question

The linear momentum of a body is increased by $200$ %. Calculate the percentage increase in kinetic energy.

Answer 1

$P$ is increased by $200\%$, hence $p_2=3p_1$

$K=\frac{1}{2}m{v}^2=\frac{p^2}{2m}$

$K_2-K_1=\frac{p_2^2-p_1^2}{2m}$

$⟹\frac{K_2-K_1}{K_1}=\frac{p_2^2-p_1^2}{p_1^2}=\frac{p_2^2}{p_1^2}-1$

$⟹\frac{\Delta K}{K_1}=3^2-1=8$

Hence, K increases by $800\%$