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Question

Consider a two particle system with particles having masses m1 and m2. If the first particle is pushed towards the centre of mass through a distance d, by what distance should be second particle be moved, so as to keep the centre of mass at the same position?

A
m1m2d
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B
d
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C
m2m1d
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D
m1m2+m1d
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Solution

The correct option is A m1m2d
If x1 and x2 are the positions of masses m1 and m2, the position of the centre of mass is given by xcm=m1x1+m2x2m1+m2
If x1 changes by Δx1 and x2 changes by Δx2, the change in xcm will be
Δxcm=m1Δx1+m2Δx2m1+m2 .........(I)
Given Δxcm=0 and Δx1=d.
Using these values in eq.(i), we get m1d+m2Δx2=0
or Δx2=m1dm2
Distance moved by m2=m1dm2, which is choice (a).

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