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A system consists of two particles of masses m1 and m2. If the first particle is displaced toward the centre of mass by a distance d, how far must the second particle be shifted to keep the centre of mass fixed at its original position?

1. (m2/m1) d
2. (m1/(m1 + m2)) d
3. (m1/m2) d
4. d

Correct answer: (m1/m2) d

Solution

To hold the centre of mass fixed the mass-weighted displacements must cancel: m1*d = m2*d2, so the second particle must move (in the opposite sense) by d2 = (m1/m2) d.

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