Question

In the non-relativistic regime, if the momentum, is increase by 100%, the percentage increase in kinetic energy is

• A. $100$
• B. $200$
• C. $300$
• D. $400$

Answer 1

The correct option is C $300$

Kinetic energy and momentum are related as
$KE=\frac{P^2}{2m}$
Momentum is increased by 100% that is $P_2=2P_1$
$K{E}^{\prime }=\frac{P_2^2}{2m}=\frac{(2P{)}^2}{2m}=4\times \frac{P^2}{2m}=4KE$
Increase in kinetic energy$4KE-KE=3KE$
Percentage increase$\frac{3KE}{KE}\times 100=300$
Option C.