Question

Let $l$ be the moment of inertia of an 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

• A. $l$
• B. $l\sin^{2}\theta$
• C. $l\cos^{2}\theta$
• D. $l\cos^{2}\frac{\theta}{2}$

Answer 1

Answer: (A)

$l$

Answer 2

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.

$I_{Z} = I_{AB} + I_{A'B'} = I_{CD} + I_{C'D'}$

[By the theorem of perpendicular axis]

$I_{Z} = 2I_{AB} = 2I_{A'B'} = 2I_{CD} = 2I_{C'D'}$ [As AB, A' B' and CD, C' D' are symmetric axis]

Hence $I_{CD} = I_{AB} = l$