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Kinetic Energy

Two bodies wi...

Question

Two bodies with masses $m_{1}$ and $m_{2}$ are moving with equal kinetic energy Their linear momenta are numerically in a ratio $P_{1} / P_{2}$ , will be:

m_{1} / m_{2}

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m_{2} / m_{1}

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\sqrt{m_{1} / m_{2}}

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m_{1}^{2}

m_{2}^{2}

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Solution

The correct option is C $\sqrt{m_{1} / m_{2}}$
$P = m \times v$
$K E = (m v^{2}) / 2 = P^{2} / 2 m$
$\frac{K E_{1}}{K E_{2}} = \frac{P_{1}^{2} \times m_{2}}{P_{2}^{2} \times m_{1}}$
$\frac{P_{1}}{P_{2}} = \sqrt{\frac{(K E_{1} \times m_{1})}{(K E_{2} \times m_{2})}}$
given ,
$K E_{1} = K E_{2}$
hence,
$P_{1} / P_{2} = \sqrt{m_{1} / m_{2}}$

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