Question

If the linear momentum is increased by $50\%$, then kinetic energy will increase by

• A. $50\%$
• B. $100\%$
• C. $125\%$
• D. $25\%$

Answer 1

Answer: (C)

$125\%$

Answer 2

Kinetic energy of the body, $K=\frac{p^{2}}{2 m}$ Since, the mass remains constant $\therefore K \propto p^{2}$ $\frac{K_{2}}{K_{1}}=\frac{p_{2}^{2}}{p_{1}^{2}}=\left[\frac{150}{100}\right]^{2}=\frac{9}{4}$ $100\left[\frac{K_{2}}{K_{1}}-1\right]=\left(\frac{9}{4}-1\right) \times 100=125 \%$