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

Answer: (C)

$I_{AB}=I_{1AB}+I_{2AB}+I_{3AB}+I_{4AB}$
$=\frac{2}{5}m{r}^2+\frac{2}{5}m{r}^2+\left(\frac{2}{5}m{r}^2+m{a}^2\right)+\left(\frac{2}{5}m{r}^2+m{a}^2\right)$
$=\frac{8}{5}m{r}^2+2m{a}^2$