Consider a sytem of two particles having masses `m_(1)` and `m_(2)`. If the particle of mass `m_(1)` is pushed towards the centre of mass of particles through a distance `d`, by what distance would the particle of mass `m_(2)` move so as to keep the mass centre of particles at the original position?

Options

A. `(m_(1))/(m_(1)+m_(2))d`
B. `(m_(1))/(m_(2))d`
C. d
D. `(m_(2))/(m_(1))d`

Answer

B

Explanation

Before -
`x_(CM)=(m_(1)x_(1)+m_(2)x_(2))/(m_(1)+m_(2))`
After - `x_(CM)=(m_(1)(x_(1)+d)+m_(2)(x_(2)+d))/(m_(1)+m_(2))`
`=(m_(1)x_(1)+m_(2)x_(2))/(m_(1)+m_(2))+(m_(1)d+m_(2)d)/(m_(1)+m_(2))`

By (i) and (ii) we get -
`(m_(1)d+m_(2)d)/(m_(1)+m_(2))=0`
`impliesm_(1)d=m_(2)dimpliesd=-((m_(1))/(m_(2)))d`
:. `m_(2)` moves towards the COM .