Two bodies have same momentum. Which will have greater kinetic energy, heavier body or lighter body?

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Solution

Let $m_{1}$ and $m_{2}$ be the masses of the body

Let $m_{1} > m_{2}$

Given that
$m_{1} v_{1} = m_{2} v_{2}$

$\frac{v_{1}}{v_{2}} = \frac{m_{2}}{m_{1}}$

$∴$ Ratio between their kinetic energies , $= \frac{K_{1}}{K_{2}} = \frac{\frac{1}{2} m_{1} v_{1}^{2}}{\frac{1}{2} m_{2} v_{2}^{2}}$

$⟹ \frac{K_{1}}{K_{2}} = \frac{m_{1}}{m_{2}} \times \frac{m_{2}^{2}}{m_{1}^{2}} = \frac{m_{2}}{m_{1}}$

This shows the Kinetic energy is greater for that mass which is lighter

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