Question

Three solid spheres each of mass $P$ and radius $Q$ are arranged as shown in figure. The moment inertia of the arrangement about $Y{Y}^{\prime }$ axis will be

• A. $\frac{7}{2}{PQ}^2$
• B. $\frac{2}{7}{PQ}^2$
• C. $\frac{2}{5}{PQ}^2$
• D. $\frac{5}{2}{PQ}^2$

Answer 1

The correct option is C $\frac{2}{5}{PQ}^2$

Moment of inertia(MOI) of sphere rotating about centre of mass$=\frac{2}{5}M{R}^2$

Using the parallel axis theorem, $I=I_{cm}+M{x}^2$, where $I_{cm}$ is MOI about centre of mass, $x$ is the distance between axis of rotation and centre of mass.

$\Rightarrow$ MOI of the arrangement about $Y{Y}^{\prime }$ Axis $=\frac{2}{5}P{Q}^2+2(\frac{2}{5}P{Q}^2+P{Q}^2)=\frac{16}{5}P{Q}^2$