Consider a uniform square plate of of side and mass `m`. The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is -

Options

A. `(1)/(12)ma^(2)`
B. `(7)/(12)ma^(2)`
C. `(2)/(3)ma^(2)`
D. `(5)/(6)ma^(2)`

Explanation

`I_(x)=I_(y)=(ma^(2))/(12)`
`I_(z)=I_(x)+I_(y)=(ma^(2))/(6)` (`bot^(ar)` axes theorem)
`OA=(a)/(sqrt2)`
`M.I.` about an axis passing through `A` and `bot^(ar)` to the plane
`I_(A)=(I_(z))_(c.m.)+m(OA)^(2)` (parallel axes theorem)
`=(ma^(2))/(6)+m((a)/(sqrt2))^(2)`
`=ma^(2)((1)/(6)+(1)/(2))=(2)/(3)ma^(2)`