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The 'e' Equation

Two bodies of...

Question

Two bodies of masses $M_{A}$ and $M_{B}$ have equal kinetic energy. The ratio of their momentum is:

A

M_{B} : M_{A}

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B

M_{A} : M_{B}

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C

{\sqrt{M}}_{A} : \sqrt{M_{B}}

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D

M_{A}^{2} : M_{B}^{2}

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Solution

The correct option is B ${\sqrt{M}}_{A} : \sqrt{M_{B}}$
$K E_{A} = K E_{B}$

$p = M v$

$p^{2} = M^{2} v^{2} = 2 M (K E)$

$p = \sqrt{2 M (K E)}$

$\frac{p_{A}}{p_{B}} = \frac{\sqrt{2 M_{A} (K E_{A})}}{\sqrt{2 M_{B} (K E_{B})}}$

$\frac{p_{A}}{p_{B}} = \frac{\sqrt{M_{A}}}{\sqrt{M_{B}}}$

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