Question

If the kinetic energy of a body is increased by 300% then determine the percentage increase in the momentum

• A. 100 %
• B. 150 %
• C. $\sqrt{300}$
• D. 175 %

Answer 1

The correct option is A 100 %

When the kinetic energy increases by $300$%,new kinetic energy will be

$K^{\prime }=K+300$%K

$K^{\prime }=K+3K$

$K^{\prime }=4K$.............(i)

We know that,

K.E, $K=\frac{P^2}{2m}$ 9$m$ is the mass of object0

Therefore, eq.(i) become

$\begin{array}{c}\frac{P{}^{\prime 2}}{2m}=4\frac{p^2}{2m}\\ p{}^{\prime 2}=4p^2\\ p^{\prime }=\sqrt{4}{p}^2\\ p^{\prime }=2p...........\left(ii\right)\end{array}$

% change in momentum $=\frac{p^{\prime }-p}{p}\times 100$

$=\frac{2p-p}{p}\times 100$%$=1\times 100=100$%

Therefore, increases in momentum is $100$%.