Three identical spherical shells, each of mass m and radius r are placed as shown in figur. Consider an axis `XX^(1)` which is touching to two shells and passing through diameter of third shell. M.I of the system consisting of these three spherial shells about `XX^(1)` axis is

Options

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

Answer

b

Explanation

Using parallel axes theorem,
`I_(xx') = I_(1) ("diameter") + I_(2) ("tangential") + I_(3) ("tangential")`
`= 2//3 mr^(2) + (2//3 mr^(2) + mr^(2)) + (2//3 mr^(2) + mr^(2))`
`=2 mr^(2) + 2mr^(2) = 4 mr^(2)`