Question

If the kinetic energy of a body increases by 125%, the percentage increase in its momentum is :

• A. $50$ %
• B. $62.5$%
• C. $250$ %
• D. $200$ %

Answer 1

The correct option is A $50$ %

Initial Kinetic energy,

$K_i=\frac{P_i^2}{2m}$

If the kinetic energy of body increased by 125%, then the final kinetic energy,

$K_f=K_i+\frac{125}{100}{K}_i$

$K_f=\frac{9}{4}{K}_i$

$\frac{P_f^2}{2m}=\frac{9}{4}\frac{P_i^2}{2m}$

$P_f=\frac{3}{2}{P}_i$

Percentage increase in momentum,

$\frac{P_f-P_i}{P_i}\times 100=(\frac{3}{2}-1)\times 100=50$%

The correct option is A.