Four spheres each of diameter `2a` and mass m are placed with their centres on the four corners of a square of the side b. Calculate the moment of inertia of the system about and side of the square.

Explanation

`I_(1)=(2)/(5)ma^(2)`
`I_(2)=(2)/(5)ma^(2)+mb^(2)`
`I_(3)=(2)/(5)ma^(2)+mb^(2)`
`I_(4)=(2)/(5)ma^(2)`
`:.` Moment of Inertia of the system I
`=I_(1)+I_(2)+I_(3)+I_(4)`
`=(2)/(5)ma^(2)+(2)/(5)ma^(2)+mb^(2)+(2)/(5)ma^(2)+mb^(2)+(2)/(5)ma^(2)`
`I=(8)/(5)ma^(2)+2mb^(2)`