Q: Let *I* be the moment of inertia of 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 plane of the plane that passes through the centre of the plate and makes an angle θ with AB. The moment of inertia of the plate about the axis CD is then equal to

(a) I

(b) I sin^{2}θ

(c) I cos^{2}θ

(d) I cos^{2} (θ/2)

Ans: (a)

Sol: Consider an axis A’B’ which is perp. to AB and axis C’D’ perp. to CD in the same Plane .

A/C to Perp. axis theorem ,

I_{ZZ’} = I_{AB} + I_{A’B’}

and , I_{ZZ’} = I_{CD} + I_{C’D’}

I_{ZZ’} = 2 I_{AB} = 2 I_{CD}

I_{AB} = I_{CD}