SATHEE: Rotational Motion Question 105

Rotational Motion Question 105

Question: Two particles $A$ and $B$ start moving due to their mutual interaction only. If at any time t, ${\vec{a}}_{A}$ and ${\vec{a}}_{B}$ are their respective accelerations, ${\vec{v}}_{A}$ and ${\vec{v}}_{B}$ are their respective velocities, and up to 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?

Options:

A) ${\vec{v}}_{A} + {\vec{v}}_{B} = 0$

B) $m_{A} {\vec{v}}_{A} + m_{B} {\vec{v}}_{B} = 0$

C) $W_{A} + W_{B} = 0$

D) ${\vec{a}}_{A} + {\vec{a}}_{B} = 0$

Show Answer

Answer:

Correct Answer: B

Solution:

[b] Since $Σ {\vec{F}}_{e x t} = \vec{0} \Rightarrow m_{A} {\vec{a}}_{A} + m_{B} {\vec{a}}_{B} = 0$

$∴$ Momentum of system will remain conserved, equal to zero.

$m_{A} {\vec{v}}_{A} + m_{B} {\vec{v}}_{B} = 0$

But $W_{A} + W_{B} \neq 0$

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