Three identical spheres, each of mass 1 kg are kept as shown in figure, touching each other, with their centres on a straight line. If their centres are marked P, Q, R respectively, the distance of centre of mass of the system from P is

Options

A. `(PQ + PR + QR)/(3)`
B. `(PQ + PR)/(3)`
C. `(PQ + QR)/(3)`
D. `(PR + QR)/(3)`

Answer

B

Explanation

`X_(CM) = ((M_(p)) (0) + (M_(Q)) (PQ) + (M_(R)) (PR))/(M_(P) + M_(Q) +M_(R))`
`= (1 xx 0 + 1 xx PQ + 1 xx PR )/(1 + 1 + 1) = (PQ + PR)/(3)`