Question

Four spheres each having mass m and radius r are placed with their centres on the four corners of a square of side a. Then the moment of inertia of the system about an axis along one of the sides of the square is:

• A. $\frac{8}{5}m{r}^2$
• B. $\frac{8}{5}m{r}^2+m{a}^2$
• C. $\frac{8}{5}m{r}^2+2m{a}^2$
• D. $\frac{4}{5}m{r}^2+4m{a}^2$

Answer 1

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

Moment of intertia of the system
$I_{AB}=I_{A{B}_1}+I_{A{B}_2}+I_{A{B}_3}+I_{A{B}_4}$
$=\frac{2}{5}m{r}^2+\frac{2}{5}m{r}^2+(\frac{2}{5}m{r}^2+m{a}^2)+(\frac{2}{5}m{r}^2+m{a}^2)$
$=\frac{8}{5}m{r}^2+2m{a}^2$