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Kinetic Energy

Two guns of m...

Question

Two guns of mass $M_{A}$ and $M_{B}$ (with $M_{A} > M_{B}$ ) fire bullets of equal mass with equal bullet velocities. If $K_{A}$ and $K_{B}$ are the recoil kinetic energy of the two guns then

A

K_{A} > K_{B}

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B

K_{A} < K_{B}

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C

K_{A} = K_{B}

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D

nothing can be said

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Solution

The correct option is B $K_{A} < K_{B}$
Since,
$E = \frac{m v^{2}}{2} = \frac{{(m v)}^{2}}{2 m} = \frac{p^{2}}{2 m}$

$E \propto \frac{1}{m} f o r c o n s t a n t p .$

$K_{A} < K_{B}$ since $M_{A} > M_{B}$

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