Let I be the moment of inertia of uniform square plane about an axis AB that passes through its centre and is parallel…

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 sin²θ

(c) I cos²θ

(d) I cos² (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