Let `I` be the moment of interia of a uniform square plate about an axis `AB` that passses through its centre and is parallel to two its sides. `CD` is a line in the plane of the plate that passes through the centre of the plate and makes an angle `theta` with `AB`. The moment of inertia of the plate about the axis `CD` is then equal to-

Options

A. I
B. `I sin^2 theta`
C. `I cos^2 theta`
D. `I cos^2(theta/2)`

Answer

A

Explanation

(a) `A'B' _|_ AB and CD' _|_ CD`
From symmetry `I_(AB)
From symmetry `I_(AB) = I_(A'B') and I_(CD) = I_(C'D')`
From theorem of
perpendicular axes,
`I_(zz) = I_(A'B') = I_(CD) + I_(C'D')`
`rArr 2I_(AB) = 2I_(CD)`
`:. I_(AB) = I_(CD)`