Question

If the $K.E$ of a body is increases by $300\%$, its momentum will increase by

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

Answer 1

The correct option is A $100\%$

Kinetic energy of body is given by,

$K=\frac{p^2}{2m}$. . . . . . .(1)

where, $m=$ mass of body

$p=$ momentum of body

when the kinetic energy is increased by 300%, then

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

$K^{\prime }=K+3K=4K$ . . . . . .(2)

from equation (1), equation (2) becomes,

$\frac{p^{\prime 2}}{2m}=4\frac{p^2}{2m}$

$p^{\prime }=2p$

Increase in momentum,

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

The correct option is A.