Three identical spheres each of mass m a...

Three identical spheres each of mass `m` and radius `R` are placed touching each other so that their centres `A,B` and `C` lie on a straight line. The position of their centre of mass from centre of `A` is

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The centre of three spheres lie at the vertices `A, B, C` of an equilibrium triangle, Fig. Centre of mass is at the centroid of `Delta ABC`.
Taking `A` as the origin, the co-ordinates of the three vertices of the triangle are :
`A (x_(1), y_(1)) = 0, 0, B(x_(2),y_(2)) = 2 r,0`
and `C (x_(3),y_(3)) = r, r sqrt(3)`
`:.` Co-ordinates of centre of mass `O` are
`x= (m(x_(1) + x_(2) + x_(3)))/(3m) = (0 + 2r + r)/(3) = r`
`y= (m(y_(1) + y_(2) + y_(3)))/(3m) = (0 + 0 + r sqrt(3))/(3) = (r)/(sqrt(3))`

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