Question

Kinetic energy of a particle is increased by 1%. By how much percentage momentum of the particle will increase?

• A. 0.25%
• B. 0.45%
• C. 0.5%
• D. 0.75%

Answer 1

Answer: (C)

0.5%

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

$⟹P=\sqrt{2M\left(KE\right)}$

The new kinetic energy is $K{E}^{\prime }=1.01KE$

Thus new momentum is $P^{\prime }=\sqrt{2M\left(K{E}^{\prime }\right)}$

$=\sqrt{2M\left(1.01KE\right)}$

$=\sqrt{1.01}P$

Thus percentage change in momentum is $\frac{P^{\prime }-P}{P}\times 100$%

$=\frac{\sqrt{1.01}-1}{1}\times 100$%=$0.5$%