Question

If the momentum of the body is increased $100$ . Then the percentage increase in the kinetic energy will be

• A. $300$
• B. $150$
• C. $75$
• D. $200$

Answer 1

Answer: (A)

Initial momentum $p_1=100p$ Final momentum $p_2=200p$ Initial kinetic energy $K_1=K$ The kinetic energy is given by $K=\frac{p^2}{2m}\propto p^2$ or $\frac{K_1}{K_2}={\left(\frac{p_1}{p_2}\right)}^2$ or $\frac{K_1}{K_2}={\left(\frac{100p}{200p}\right)}^2=\frac{1}{4}$ $K_2=4K_1$ Increase in kinetic energy is $=4K_1-K_1=3K_1=300$