Question

Three identical spheres, each of mass $ 1\,kg $ are kept as shown in figure below, 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:

• A. $ \frac{PQ+PR+QR}{3} $
• B. $ \frac{PQ+PR}{3} $
• C. $ \frac{PQ+QR}{3} $
• D. $ \frac{PR+QR}{3} $
• E. $ \frac{PQ+QR+PR}{6} $

Answer 1

Answer: (B)

$ {{r}_{1}}=0,{{r}_{2}}=PQ,{{r}_{3}}=PR $
Distance of centre of mass from P is
$ r=\frac{{{r}_{1}}+{{r}_{2}}+{{r}_{3}}}{3} $
$ =\frac{0+PQ+PR}{3} $
$ =\frac{PQ+PR}{3} $