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Question

# Consider a two - particle system with the particle 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 the second particle be moved to keep the centre of mass at the same position ?

A
m1m2d
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B
m2m1d
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C
m1+m2m2d
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D
m1m2m1+m2d
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Solution

## The correct option is A m1m2dConsider the following diagram where we are having the two masses m1 and m2 and the centre of mass is at C. Let x1 be the distance of m1 from point C and x2 be the distance of m2 from C. Now let m1 be pushed towards point C through a distance d and let m2 be pushed through a distance d′ to keep the centre of mass at C. In the first case we have centre mass equal because of equal masses and it is at the point C. m1x1=m2x2 ......(1) In the second case we have, we moved both the masses through distances d and d′, m1(x1−d)=m2(x2−d′) m1x1−m1d=m2x2−m2d′ ......(2) Subtracting eq.(2) from eq.(1) we get, m1x1−m1x1+m1d=m2x2−m2x2+m2d′ ⇒m1d=m2d′ ⇒d′=m1m2d Hence, option (a) is the correct answer.

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