Q. If the $K.E.$ of a body is increased by 300%, its momentum will increase by

A) 100%
B) 150%
C) $\sqrt{300}\%$
D) 175%
Explanation

(a) Let initial kinetic energy, $E_{1} = E$
Final kinetic energy, $E_{2} = E + 300\%$ of $E = 4E$
As $P \propto \sqrt{E} \Rightarrow \frac{P_{2}}{P_{1}} = \sqrt{\frac{E_{2}}{E_{1}}} = \sqrt{\frac{4E}{E}} = 2 \Rightarrow P_{2} = 2P_{1}$
$\Rightarrow P_{2} = P_{1} + 100\%$ of $P_{1}$
$i.e$., Momentum will increase by 100%

Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

Ph.D. in Physics with 19+ years of teaching experience.