Question

Four spheres, each of mass $m$ and radius $r$, are placed with their centres on the four corners of a square of side $b$. The moment of inertia of the system about any side of the square is

• A. $\frac{8}{5}m{r}^2+m{b}^2$
• B. $\frac{8}{5}m{r}^2+2m{b}^2$
• C. $\frac{8}{5}m{r}^2+4m{b}^2$
• D. None of these

Answer 1

Answer: (B)

$\frac{8}{5}m{r}^2+2m{b}^2$

Moment or Inertia of two spheres lying on the axis is $2\times \frac{2}{5}m{R}^2=\frac{4}{5}m{R}^2$

Using parallel axis of theorem

Moment of Inertia of two sphere lying on the edge parallel to the axis at a distance of b:

$2(\frac{2}{5}m{R}^2+m{b}^2)=\frac{4}{5}m{R}^2+2m{b}^2$

Therefore total moment of inertia is

$\frac{4}{5}m{R}^2+2m{b}^2+\frac{4}{5}m{R}^2=\frac{8}{5}m{R}^2+2m{b}^2$