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

The correct option is B $\frac{8}{5}m{r}^2+2m{b}^2$

$I=\left(\frac{2}{5}m{r}^2\right)\times 2+2[\frac{2}{5}m{r}^2+m{b}^2]$

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

Hence, the answer is $\frac{8}{5}m{r}^2+2m{b}^2.$