Question

A light body and a heavy body have the same kinetic energy. Which one will have greater momentum?

Answer 1

Relationship between kinetic energy and momentum

The relation between kinetic energy and momentum is given as,

$KE=\frac{p^2}{2m}$

where $KE$ is kinetic energy, $p$ is momentum and $m$ is mass.

Finding how momentum varies with mass when kinetic energy is constant

From $KE=\frac{p^2}{2m}$, it can be said that,

$p=\sqrt{2mKE}$

If kinetic energy is constant, it can be said that,

$p\propto \sqrt{m}$

Hence, momentum is directly proportional to mass. In other words, the greater the momentum, the greater will be the mass, and vice versa.

Therefore, for two bodies of unequal masses that have the same kinetic energy, the heavier body will possess a greater momentum.