Question

If the linear momentum of a body is increased by $50$% then K.E of the body will increase by

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

Answer 1

The correct option is C $125$%

We know that $P=\sqrt{2mK}$
or $K\propto P^2$

$\frac{K_2}{K_1}=\frac{{P_2}^2}{{P_1}^2}$

or $\frac{K_2-K_1}{K_1}\times 100=\left(\frac{{P_2}^2-{P_1}^2}{{P_1}^2}\right)\times 100$

% increase $=\left(\frac{{150}^2-{100}^2}{{100}^2}\right)\times 100$

$=\frac{250\times 50}{100}=125$%