Question

A light body and a heavy body have equal kinetic energy. Which one has a greater momentum?

Answer 1

from given kinetic energies are equal

$\frac{1}{2}{m}_1{v_1}^2=\frac{1}{2}{m}_2{v_2}^2$ $(m_2>m_1)$ where $m_1$ = mass of lighter body & $m_2$ = mass of the heavier body

$\frac{{v_1}^2}{{v_2}^2}=\frac{m_2}{m_1}⟹\frac{v_1}{v_2}=\sqrt{\frac{m_2}{m_1}}$

linear momentum of a lighter body $P_1=m_1{v}_1$

linear momentum of the heavier body $P_2=m_2{v}_2$

$\frac{P_1}{P_2}=\frac{m_1{v}_1}{m_2{v}_2}=\frac{m_1}{m_2}\sqrt{\frac{m_2}{m_1}}=\sqrt{\frac{m_2}{m_1}\times \frac{{m_1}^2}{{m_2}^2}}=\sqrt{\frac{m_1}{m_2}}$

here linear momentum is directly proportional to its mass

$\therefore$ heavierbody has greater momentum