Question

If the linear momentum of a body is increased by $50\%$, the Kinetic energy will be increased by

Answer 1

the relation between linear momentum and kinetic energy

$K.E=\frac{P^2}{2m}$

$P_1=P$

$P_2=P+\frac{p}{2}$ = $\frac{3P}{2}$

$K.E_1=\frac{P^2}{2m}$

$K.E_2=\frac{(\frac{3P}{2}{)}^2}{2m}$ = $\frac{\frac{9P^2}{4}}{2m}$

change in $K.E=\frac{9P^2}{4}-P^2=\frac{5P^2}{4}$

% increase in $K.E=\frac{5P^2}{4}\times 100=125$%