Let l be the moment of inertia of a uniform square plate about an axis AB that passes through its centre and is parallel to two of 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. l
B. `I sin^(2)theta`
C. `I cos^(2)theta`
D. `I cos^(2)(theta//2)`

Answer

A

Explanation

`A'B' bot AB` and `C'D' bot CD`
From theorem of perpendicular axis,
`I_(ZZ) = I_(AB) + I_(A'B') = I_(CD) + I_(CD') rArr 2I_(AB) = 2I_(CD) therefore I_(AB) = I_(CD)`