Question

Three identical spheres each of mass $1$kg are placed touching one another with their centres in a straight line. Their centres are marked as A, B, C respectively. The distance of centre of mass of the system from A is.

• A. $\frac{AB+AC}{2}$
• B. $\frac{AB+BC}{2}$
• C. $\frac{AC-AB}{3}$
• D. $\frac{AB+AC}{3}$

Answer 1

The correct option is D $\frac{AB+AC}{3}$

Center of mass of the system lies at the center of the sphere B.

Center of mass of system $x=\frac{M_A{x}_A+M_B{x}_B+M_C{x}_C}{M+M+M}$

$\therefore$ $x=\frac{M\left(0\right)+M\left(AB\right)+M\left(AC\right)}{3M}$

$⟹$ $x=\frac{AB+AC}{3}$