A light body and a heavy body have same linear momentum. Which one has greater Kinetic Energy?

Let $P_1$ and $P_2$ be the linear momentum and kinetic energy $E_1$ and $E_2$ of light and heavy body respectively.

According to question,

$P_1 = P_2$

i.e., $m_1\; v_1 = m_2\; v_2$

or, $\frac{v_2}{v_1} = \frac{m_1}{m_2}$ .......... (i)

Again,

$E_1 = $$\frac{1}{2}$$m_1\; v_{1}^{2}$

$E_2 = $$\frac{1}{2}$$m_2\; v_{2}^{2}$

or, $\frac{E_2}{E_1} = \frac{\frac{1}{2}m_2 v_{2}^{2}}{\frac{1}{2}m_1 v_{1}^{2}} = \frac{m_2}{m_1} (\frac{v_2}{v_1})^2$

or, $\frac{m_2}{m_1} (\frac{m_1}{m_2})^2 = \frac{m_1}{m_2}$

If $m_1$ is mass of light body and $m_2$ be the mass of heavy body. Then,

$m_1 < m_2$, $E_2 < E_1$

or, $E_1 > E_2$ .......... (ii)

∴ From equation (ii) we conclude that, the lighter body has more Kinetic Energy.