Three identicle particle each of mass `1 kg` are placed with their centres on a straight line. Their centres are marked `A, B and C` respectively. The distance of centre of mass of the system from `A` is.

Options

A. `(AB+AC)/(2)`
B. `(AB+BC)/(2)`
C. `(AC-AB)/(3)`
D. `(AB+AC)/(3)`

Answer

D

Explanation

A, B and C are the centres of the three spheres and the distances are measured from A. As all centres are in a straight line, we will consider only the x- cordinates of all.
`therefore X_(xm)=(m_(1)x_(1)+m_(2)x_(2)+m_(3)x_(3))/(m_(1)+m_(2)+m_(3))`
`=(1xx0+1xxABxx1xxAC)/(1+1+1)`
`=(AB+AC)/(3)`
and hence `X_(cm)` is at a distance `(AB+AC)/(3)` from A.