Question

The moment of inertia of thin square plate `ABCD` of uniform thickness about an axis passing through the center `O` and perpendicular to the plane of the plate is

(`i`) `I_(1)+I_(2)`
(`ii`) `I_(2)+I_(4)`
(`iii`) `I_(1)+I_(3)`
(`iv`) `I_(1)+I_(2)+I_(3)+I_(4)`
where `I_(1)`, `I_(2)`, `I_(3)` and `I_(4)` are repectively moments of inertia about axes `1`, `2`, `3` and `4` which are in the plane of the plane
A. (`i`),(`ii`)
B. (`i`), (`ii`), (`iii`)
C. (`ii`), (`iii`)
D. (`i`), (`iii`)

Answer 1

As explained in the previous problem
`I_(1)=I_(2)=I_(3)=I_(4)`
`I_(0)=I_(1)+I_(2)=I_(2)+I_(4)` (`bot^(ar)` axes theorem)
`=I_(1)+I_(3)`