Five solid spheres each of mass $m$ and radius $r$ are rotating about an axis $A$ as shown in figure. Hence…
Five solid spheres each of mass $m$ and radius $r$ are rotating about an axis $A$ as shown in figure. Hence the moment of inertia of the system about the axis of rotation A-A' as shown in figure. Hence the moment of inertia of the system about the axis of rotation A-A' is
$6 m r^2$
$5 m r^2$
$3 m r^2$
$4 m r^2$
Solution
Moment of inertia of a sphere about diameter is $\frac{2}{5} m r^2$
Moment of inertia of a sphere about it tangent using parallel axis theorem
$\begin{aligned} & I=I_{\mathrm{am}}+m r^2=\frac{2}{5} m r^2+m r^2=\frac{7}{5} m r^2 \\ & I_{\text {total }}=3\left(\frac{2}{5} m r^2\right)+2\left(\frac{7}{5} m r^2\right)=\frac{20}{5} m r^2=4 m r^2\end{aligned}$
