Question

Three identical spherical shells, each of mass m and radius r are placed as shown in figure. Consider an axis X X' 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 XX' axis is

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

Answer 1

Answer: (B)

$4 m r^2$

Answer 2

Net moment of inertia of the system, $I = I_1 + I_2 + I_3$ The moment of inertia of a shell about its diameter, $I_1 = \frac{2}{3} mr^2$ The moment of inertia of a shell about its tangent is given by $I_2 = I_3 = I_1 + mr^2 = \frac{2}{3} mr^2 + mr^2 = \frac{5}{3} mr^2$ $\therefore I = 2 \times \frac{5}{3} mr^2 + \frac{2}{3} mr^2 = \frac{12mr^2}{3} = 4mr^2$