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

Explanation

Let `I_z` is the moment of inertia of square plate about the axis which is passing through the centre and perpendicular to the plane `I_z=I_(AB)+I_(A.B.)=21_(CD)=21_(C.D.)`[By the theorem of prependicular axis] `I_z=21_(AB)=21_(A.B.)=21_(CD)=21_(C.D.)`[AS AB,A.B. and C.D.are symmetric axis].Hence` I_(CD)=I_(AB)=l`.