Question

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

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

Answer 1

Answer: (D)

Total moment of inertia of the system,
$I=I_{1}+I_{2}+I_{3}$
$I_{2}=I_{3}=\frac{2}{3}mr^{2}+mr^{2}=\frac{5 m r^{2}}{3}$
$I_{1}=\frac{2}{3}mr^{2}$
$\therefore I=2\times 5\frac{m r^{2}}{3}+\frac{2}{3}mr^{2}$
$=\frac{12 m r^{2}}{3}=4mr^{2}$