The moment of inertia of a rectangular laminate ABCD about $O = \frac{a^{2} + b^{2}}{12},$ along an axis perpendicular to the laminate, passing through the centre of mass O. Select the wrong Statement about the moment of inertia about an axis perpendicular to the plane.

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Passing through B is greater than that through O but smaller than that through H

Passing through B > through F > through O

The moment of inertia will be same if this had been a thick block

The moment of inertia $I_{z}$ is always greater than $I_{x} a n d I_{y}$ because $I_{z} = I_{x} + I_{y}$

answer is A.

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Detailed Solution

The parallel axes theorem gives that $I_{0} + M O B^{2}$ is having the greatest value compared
to O, F, G, H, E.
For block also it is valid.
Here, it is valid but not valid for a sphere, thin cylindrical rod etc. The perpendicular axes theorem is not always valid. It depends on the shape.

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