Two particles of masses m and 3m are initially at rest on a smooth horizontal surface and are separated by distance L. Due only to mutual internal forces, they move toward each other and meet. The distance moved by the particle of mass m before they meet is:
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Question

Two particles of masses m and 3m are initially at rest on a smooth horizontal surface and are separated by distance L. Due only to mutual internal forces, they move toward each other and meet. The distance moved by the particle of mass m before they meet is:

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G1 Physics · Accepted Answer

With no horizontal external force, the centre of mass remains fixed. Place mass m at x=0 and mass 3m at x=L. Initially x(CM) = [m(0)+3m(L)]/(4m) = 3L/4. When the particles meet, they must meet at the fixed centre-of-mass position. Therefore the mass m moves from x=0 to x=3L/4, a distance 3L/4.