Question

Three identical spherical shells, each of mass $2kg$ and radius $10cm$ are placed as shown in figure. Consider an axis $X{X}^{\prime }$ which is touching to two shells and passing through diameter of third shell. Moment of inertia of the system consisting of these three spherical shells about $X{X}^{\prime }$ axis is _______$kg{m}^2$.

Answer 1

Answer: 0.08

Using parallel axes theorem,
$I_1=\frac{2}{3}m{r}^2+m{r}^2$ and $I_1=I_2$
$I_3=\frac{2}{3}{m}^2$
$\therefore M.I$. of system about $X{X}^{\prime }$ is
$I=I_1+I_2+I_3$
$=2\left(\frac{2}{3}m{r}^2+m{r}^2\right)+\frac{2}{3}m{r}^2$
$=4m{r}^2=4\times 2\times {\left(10\times 10^{-2}\right)}^2$
$=8\times 10^{-2}$
$\therefore I=0.08kg{m}^2$