Which of the following is/are correct?

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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, then there must be some net work being done on the system outside.

answer is A.

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Detailed Solution

1. As ΣP→=0 and P→1+P→2≠0, P→3 cannot be zero.2. For any system of two or more than two particles, KE can change due to work done by internal forces while the centre of mass remains at rest 3. a→CM=0⇒ΣF→ext=04. It is possible to have changing speed of CM without any work done by ext. forces on the system. When a person accelerates himself on a rough horizontal surface without any slipping between his shoes and ground, work done by friction, normal reaction and weight all are zero but speed of centre of mass changes.

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