Question

Momentum of a particle is increased by $50$%. By how much percentage kinetic energy of particle will increase?

• A. $50$
• B. $75$%
• C. $125$%
• D. $150$%

Answer 1

The correct option is C $125$%

Kinetic energy of a particle $KE$ in terms of momentum $P$ is $KE=\frac{P^2}{2M}$.

The new momentum be $P^{\prime }=1.5P$

Thus new kinetic energy is $K{E}^{\prime }=\frac{P^{\prime 2}}{2M}={1.5}^2\frac{P^2}{2M}$

$={1.5}^{2}KE=2.25KE$

Thus percentage increase in kinetic energy is $\frac{K{E}^{\prime }-KE}{KE}\times 100$%=$\frac{2.25-1}{1}\times 100$%=$125$%