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Question

A system of two particles is having masses m1 and m2. If the particle of mass m1 is pushed towards the center of mass of particles through a distance, d, then determine by what distance the particle of mass m2 should be moved so as to keep the centre of mass of particles at the original position?

A
m1m2+m2d
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B
d
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C
m1m2d
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D
m2m1d
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Solution

The correct option is C m1m2d
Position of center of mass xcm=m1x1+m2x2m1+m2

Shift in position of center of mass Δxcm=m1Δx1+m2Δx2m1+m2

Given : Δxcm=0 Δx1=d

0=m1d+m2Δx2m1+m2

Δx2=m1m2d

Thus m2 must also be shifted towards the center of mass by a distance m1m2d.

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