If two bodies, one light and other heavy have equal kinetic energies, which one has a greater momentum?

Heavy body

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Light body

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Both have equal momentum

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It depends on the actual velocities

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Solution

The correct option is B Light body
$K . E_{1} = \frac{1}{2} m_{1} v_{1}^{2}$

$K . E_{2} = \frac{1}{2} m_{2} v_{2}^{2}$

Given that

$K . E_{1} = K . E_{2}$

$m_{1} v_{1}^{2} = m_{2} v_{2}^{2}$

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

$\frac{m_{1} v_{1}}{m_{2} v_{2}} = \sqrt{\frac{m_{1}}{m_{2}}} = \sqrt{\frac{2}{8}} = \frac{1}{2} = 0.5$

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