`ABCD` is a square plate with centre `O`. The moments of inertia of the plate about the perpendicular axis through `O` is `I` and about the axes `1, 2, 3, & 4` are `I_(1),I_(2),I_(3) & I_(4)` respectively. It follows that :
.

Options

A. `I_(2) = I_(3)`
B. `I = I_(1) + I_(4)`
C. `I = I_(2) + I_(4)`
D. `I_(1) = I_(3)`

Answer

A, B, C, D

Explanation

From perpendicular axis theorem
`I = I_(1) + I_(3)` or `I = I_(2) + I_(4)`
From symmetry `I_(1) = L_(3)` and `I_(2) = I_(4)`
so, `I_(1) = I_(2) = I_(3) = I_(4)`
Therefore
(A) `I_(2) = I_(3)`
(B) `I = I_(1) + I_(4)`
( c) `I = I_(2) + I_(4)`
(D) `I_(1) = I_(3)`.