Question

Three identical spherical shells, each of mass $m$ and radius $r$ are placed as shown in the figure. Consider an axis $X{X}^{\prime }$ which is touching the two shells and passing through the diameter of the third shell. The moment of inertia of the system consisting of these three spherical shells about $X{X}^{\prime }$ axis is:

• A. $\frac{11}{5}m{r}^2$
• B. $3m{r}^2$
• C. $\frac{16}{5}m{r}^2$
• D. $4m{r}^2$

Answer 1

Answer: (D)

Total moment of inertia of the system,
$I=I_1+I_2+I_3$
$I_2=I_3=\frac{2}{3}m{r}^2+m{r}^2=\frac{5m{r}^2}{3}$
$I_1=\frac{2}{3}m{r}^2$
$\therefore I=2\times 5\frac{m{r}^2}{3}+\frac{2}{3}m{r}^2$
$=\frac{12m{r}^2}{3}=4m{r}^2$