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

`_(Z)= I_(AB) + I_(A.B.)`
also, `I_(Z) = I_(CD) + I_(CD)`
as `I_(A.B.) = I_(CD) = I_(C.D.)= I`