Find the momentof inertia of a uniform square plate of mass m and edge a about one of its diagonals.

Explanation

`I_(1-1)=?`
We know, for square plate
`I_(x)=I_(y)=(ma^(2))/(12)`
`I_(x)+I_(y)=I_(z)` (`bot^(ar)` axes theorem) (`i`)
Diagonals of squares are `bot^(ar)`
`I_(1-1)+I_(2-2)=I_(z)` (`ii`)
`I_(1-1)+I_(2-2)=I_(x)+I_(y)=I_(z)`
By symmetry `I_(1-1)=I_(2-2)`
`I_(1-1)=I_(2-2)=I_(x)=I_(y)=(ma^(2))/(12)`
For any axis passing through the center of plate and lying in the `x-y` plane
`I_(3-3)=I_(4-4)=(ma^(2))/(12)`