Questions

Three identical spherical shells, each of mass m and radius r are placed as shown in figure. Consider an axis $X{X}^{1}$ 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 $X{X}^{1}$ axis is:

a

$3m{r}^{2}$

b

$\frac{16}{5}m{r}^{2}$

c

$4m{r}^{2}$

d

$\frac{11}{5}m{r}^{2}$

detailed solution

Correct option is C

Moments of inertia of the shells about the given axis are

${I}_{1}=\frac{2}{3}m{r}^{2};$

${I}_{2}={I}_{3}=\frac{2}{3}m{r}^{2}+m{r}^{2}=\frac{5}{3}m{r}^{2}$ ........by parallel axis theorem

$I={I}_{1}+{I}_{2}+{I}_{3}$

$I=4m{r}^{2}$

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