Question

If the kinetic energy of a body becomes 4 times its initial value, the final momentum will be ______.

• A. same as the initial momentum
• B. twice the initial momentum
• C. four times the initial momentum
• D. eight times the initial momentum

Answer 1

The correct option is B twice the initial momentum

Consider ‘$m$’ to be the mass of the body,
‘$v$’ be the velocity of the body with which the body moves.

The kinetic energy of the body, $K.E=\frac{1}{2}m{v}^2$

The momentum of the body is given as, $P=mv$
$P^2=2m\times K.E.$

$P$ is proportional to the square root of kinetic energy, since $m$ is considered a constant.

Therefore, for the kinetic energy to increase by four times, the momentum should have to be doubled, i.e. the final momentum needs to be twice the initial momentum.