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KE and Frame of Reference

Two particles...

Question

Two particles A and B start moving due to their mutual interaction only. If at any time 't', $_{A}$ and $_{B}$ are their respective accelerations, ${\to v}_{A}$ and ${\to v}_{B}$ are their respective velocities, and upto that time $W_{A}$ and $W_{B}$ are the work done on A and B respectively by the mutual force. $m_{A}$ and $m_{B}$ are their masses respectively, then which of the following is always correct.

A

{\to v}_{A} + {\to v}_{B} = 0

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B

m_{A} {\to v}_{A} + m_{B} {\to v}_{B}

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C

W_{A} + W_{B} = 0

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D

{\to a}_{A} + {\to a}_{B} = 0

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Solution

The correct option is B $m_{A} {\to v}_{A} + m_{B} {\to v}_{B}$
$\begin{matrix} N e t m o m e n t u m w i l l b e z e r o ∴ m_{A} {\to v}_{A} + m_{B} {\to v}_{B} = 0 H e n c e, o p t i o n B i s c o r r e c t a n s w e r . \end{matrix}$

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