Three identical hollow sphere, each of mass 2 kg and radius 10 cm are placed as shown in diagram.Consider an axis XX' which is touching to two shells and passing through diameter of third shell. Calculate Moment of inertia of the system consisting of these three spherical shells XX' axis in kg `m^(2)` ?

Answer

`0.08`

Explanation

Using parallel axes theorem,
`I_(1)=(2)/(3)mr^(2) +mr^(2) and I_(1) =I_(2)`
`I_(3) =(2)/(3)m^(2)`
M.I. of system about XX. is
`I= I_(1) +I_(2) +I_(3)`
`=2 ((2)/(3) mr^(2) +mr^(2)) +(2)/(3) mr^(2)`
`=4mr^(2) = 4 xx 2 xx (10 xx 10^(-2))^(2)`
`=8 xx 10^(-2)`
`:.I=0.08kgm^(2)`