Question

Four spheres, each of mass 'M' and radius 'r' are situated at the four corners of square of side 'R'. The moment of inertia of the system about an axis perpendicular to the plane of square and passing through its centre will be

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

M. I. of sphere A about its diameter $I_{O^{\prime }}=\frac{2}{5}M{r}^2$
Now M.I. of sphere A about an axis perpendicular to the plane of square and passing through its centre will be
$I_O=I_{O^{\prime }}+M{\left(\frac{R}{\sqrt{2}}\right)}^2=\frac{2}{5}M{r}^2+\frac{M{R}^2}{2}$
Moment of inertia of system (i.e. four sphere) $=4I_O=4[\frac{2}{5}M{r}^2+\frac{M{R}^2}{2}]=\frac{2}{5}M[4r^2+5R^2]$