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Which of the following statements is incorrect? A. If the centre of mass of three particles is at rest, and it is known that two of them are moving along different non-parallel lines, then the third particle must also be moving. B. If the centre of mass remains at rest, then the net work done by the forces acting on the system must be zero. C. If the centre of mass remains at rest, then the net external force must be zero. D. None of these statements is incorrect.

1. If the centre of mass of three particles is at rest, and it is known that two of them are moving along different non-parallel lines, then the third particle must also be moving.
2. If the centre of mass remains at rest, then the net work done by the forces acting on the system must be zero.
3. If the centre of mass remains at rest, then the net external force must be zero.
4. None of these statements is incorrect.

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

Solution

If the centre of mass is at rest, its velocity is constant (zero), so the net external force on the system is zero. However, zero net external force does not imply that the net work done on the system is zero, because internal forces and energy exchanges can still occur. Hence statement B is incorrect.

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