Question

If the linear momentum is increased by $50$% then kinetic energy will be increased by

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

Answer 1

The correct option is C $125$%

$\to$ As momentum (P) and

kinetic energy (K) are

related by,

$K=\frac{P^2}{2m}$

let original = $K_1,P_1$

New = $K_2,P_2$

$\Rightarrow P_2=P_1+\frac{50}{100}{P}_1=\frac{3}{2}{P}_1$

$\Rightarrow K_2=\frac{P_2^2}{2m}=\frac{9}{4}\frac{P_1^2}{2m}=\frac{9}{4}{K}_1$

% increase = $\frac{K_2-K_1}{K_1}\times 100$

$=(\frac{9}{4}-1)\frac{K_1}{K_1}\times 100=\frac{5}{4}\times 100\%$

$=125\%\Rightarrow \left(C\right)$