Question

If momentum of a particle increased $30\%$, then increase in its kinetic energy is:

• A. 30%
• B. 60%
• C. 69%
• D. 80%

Answer 1

Answer: (C)

Momentum $p\propto \sqrt{E}$
$\frac{p_1}{p_2}=\sqrt{\frac{E_1}{E_2}}$
$\frac{p}{p+\frac{3p}{10}}=\sqrt{\frac{E_1}{E_2}}$
$\therefore \frac{10}{13}=\sqrt{\frac{E_1}{E_2}}$
$\therefore \frac{E_1}{E_2}=\frac{100}{169}$
$\therefore$ increase in kinetic energies $=69\%$