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Concepts Of Physics MCQ Edition [Volume 1]PhysicsCentre of Mass, Linear momentum, Collision

Evaluate the following two statements: (A) The linear momentum of the system is constant. (B) The centre of mass of the system is at rest.

Options

  1. AA implies B and B implies A
  2. BB implies A but A does not imply B
  3. CA implies B but B does not imply A
  4. DA does not imply B and B does not imply A

Correct answer

B. B implies A but A does not imply B

Step-by-step solution

The linear momentum of a system is given by P = M v _ cm , where M is the total mass and v _ cm is the velocity of the centre of mass. If the centre of mass is at rest (Statement B), then v _ cm = 0 . This gives P = 0 , which is a constant. Thus, B implies A. If the linear momentum of the system is constant (Statement A), then v _ cm is a constant vector. This constant velocity can be non-zero, meaning the centre of mass may not be at rest. Thus, A does not imply B. Therefore, B implies A but A does not imply B.

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