Three indentical shperical shells, each of mass m and radius r are placed as shown in figure. Consider an axis xx' 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

Options

A. `(11)/(5)mr^(2)`
B. `3 mr^(2)`
C. `(16)/(5)mr^(2)`
D. `4 mr^(2)`

Answer

D

Explanation

Moment of inertia of any spherical shell with respect to its diameter = `(2)/(3)mr^(2)`
and moment of inertia with respect to tangent
= `(2)/(3) mr^(2) + mr^(2) = (5)/(3) mr^(2)`
Hence, moment of inertia of the whole system
= `(2)/(3)mr^(2) + 2 xx (5)/(3) mr^(2) = 4 mr^(2)`