Question

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

• A. $\frac{P Q+P R+Q R}{3}$
• B. $\frac{P Q+P R}{3}$
• C. $\frac{P Q+Q R}{3}$
• D. $\frac{P R+Q R}{3}$

Answer 1

Answer: (B)

$X_{ CM } =\frac{\left(M_{P}\right)(0)+\left(M_{Q}\right)(P Q)+\left(M_{R}\right)(P R)}{M_{P}+M_{Q}+M_{R}} $
$=\frac{1 \times 0+1 \times P Q+1 \times P R}{1+1+1}=\frac{P Q+P R}{3} $