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

Explanation

`CM=(m_(1)x_(1)+m_(2)x_(2))/(m_(2)+m_(2)`
Again, `CM=(m_(1)(x_(1)-d)+m_(2)(x_(2)+d_(2)))/(m_(1)+m_(2))`
or `(m_(1)x_(1)+m_(2)x_(2))/(m_(1)+m_(2))=(m_(1)x_(1)-m_(1)d+m_(2)x_(2)+m_(2)d_(2))/(m_(1)+m_(2))`
or `m_(2)d_(2)=m_(1)d` or `d_(2)=(m_(1))/(m_(2))d`