The centre of mass of a system of two particles of masses `m_(1)andm_(2)` is at a distance `a_(1)`, from mass `m_(1)` and at a distance `a_(2)` from mass `m_(2)` such that :

Options

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

Answer

A

Explanation

Sum of moments about centre of mass is zero
`therefore m_(1)(+a_(1))+m_(2)(-a_(2))=0`

`m_(1)a_(1)=m_(2)a_(2)implies (a_(1))/(a_(2))=(m_(2))/(m_(1))`