Three idential spherical shells each of mass `m` and radius `r` are placed as shown in Fig. Consider an axis XX' which is touching the two shells and passing through diameter of third shell. Moment of Inertia of the system consisting of these three spherical shells about XX' as axis is :

Options

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

Answer

D

Explanation

The total moment of inertia of the system is
`I=I_(1)+I_(2)+I_(3)`...(i)

Here, `I_(1)=(2)/(3) mr^(2)`
`I_(2)=I_(3)=(2)/(3)mr^(2)+mr^(2)` (From parallel axis theorem)
`= (5)/(3)mr^(2)`
From Eq. (i),
`I=(2)/(3)mr^(2)+2xx(5)/(3)mr^(2)=mr^(2)((2)/(3)+(10)/(3))rArrI=4mr^(2)`.