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Which of the following is/are incorrect?

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If centre of mass of three particles is at rest and it is known that two of them are moving along different lines then the third particle must also be moving.

If centre of mass remains at rest, then net work done by the forces acting on the system must be zero.

If centre of mass remains at rest then the net external force must be zero.

If speed of centre of mass is changing the n there must be somework being done by internal forces on the system.

answer is D.

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Detailed Solution

$(i)$ Given $m_{1} {\vec{v}}_{1} + m_{2} {\vec{v}}_{2} + m_{3} {\vec{v}}_{3} = 0$

but $m_{1} {\vec{v}}_{1} + m_{2} {\vec{v}}_{2} \neq 0$

so, ${\vec{v}}_{3}$ cannot be zero

$(i i)$ work is a scalar quantity. So, sum of work done on individual particles can have any value.

$(i i i)$ ${\vec{F}}_{ext} = M ({\vec{A}}_{cm})$

because $({\vec{A}}_{c m}) = 0$ , so, ${\vec{F}}_{ext} = 0$

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