Question

Three identical spheres each of mass $1kg$ 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 $\frac{AB+AC}{3}$

The distance is to be measured from $A$
$\therefore$ Origin will be at $A$.
Now, for $CM=\frac{m_1{x}_1+m_2{x}_2+m_3{x}_3}{m_1+m_2+m_3}$
For the above figure
$CM=\frac{1\times 0+1\times AB+1\times AC}{1+1+1}$
$=\frac{AB+AC}{3}$