Question

Three idential spheres, each of mass 1 kg are placed touching each other with their centres on a straight line. Their centre are marked P, Q and R respectively. The distance of centre of mass of the system from P is

• A. $\frac{PQ+PR+QR}{3}$
• B. $\frac{2}{3}PQ+PR$
• C. $\frac{PQ+QR}{3}$
• D. none of these

Answer 1

The correct option is B $\frac{2}{3}PQ+PR$

Taking P as the origin and the line $PQ$ as the $x-axis$ then we will get the coordinate as

$P(0,0)$

$Q(PQ,0)$

$R(PR,0)$

so the center of mass will be at $x=\frac{m\times 0+m\times PQ+m\times PR}{m+m+m}=\frac{2}{3}(PQ+PR)$