Three identical spherical shells , each of mass m and radius r are placed as shown in figure . Consider an axis `XX'` which is touching 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. `(16)/(5) mr^(2)`
B. `4 mr^(2)`
C. `(11)/(5) mr^(2)`
D. `3 mr^(2)`

Answer

B

Explanation

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 = (2)/(3) mr^(2)`
The moment of inerita of a shell about its tangent is given by
`I_(2) = I_(3) = I_(1) + mr^(2) = (2)/(3) mr^(2) + mr^(2) = (5)/(3) mr^(2)`
`therefore I = 2 xx (5)/(3) mr^(2) + (2)/(3) mr^(2) = (12 mr^(2))/(3) = 4 mr^(2)`