Question

There identical uniform solid spheres each of mass ' $m$ ' and radius ' $r$ ' are joined as shown in the figure, with centers lying in the same plane. The moment of inertia of the system about an axis lying in that plane and passing through the center of sphere $C$ is

• A. $\frac{16}{5}m{r}^2$
• B. $\frac{12}{5}m{r}^2$
• C. $4m{r}^2$
• D. $\frac{3}{5}m{r}^2$

Answer 1

Answer: (A)

Moment of inertia of each solid sphere,
$I=\frac{2}{5}m{r}^2$

where, $m=$ mass and $r=$ radius .
The moment of inertia of the system about axis $PQ$ as shown in the figure.
$I_{PQ}=I_A+I_B+I_C$
$=\left[\left(\frac{2}{5}m{r}^2\right)+m{r}^2\right]+\left[\left(\frac{2}{5}m{r}^2\right)+m{r}^2\right]+\left[\frac{2}{5}m{r}^2\right]$
$=\frac{7}{5}m{r}^2+\frac{7}{5}m{r}^2+\frac{2}{5}m{r}^2$
$=\frac{16}{5}m{r}^2$