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

Answer

D

Explanation

The total moment of inertia of the system
`l=l_(1)+l_(2)+l_(2)" ….(i)"`
Here, `l_(1)=(2)/(3)mr^(2) and l_(2)=l_(3)=(2)/(3)mr^(2)+mr^(3)`
[From parallel axis theorem]
`=(5)/(3)mr^(2)`
From Eq. (i),
`l=(2)/(3)mr^(2)+2xx(5)/(3)mr^(2)=mr^(2)((2)/(3)+(10)/(3))=4mr^(2)`