The moment of inertia of a rectangular plate | vedclass

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Question

(A) According to the perpendicular axis theorem,the moment of inertia of a planar body about an axis perpendicular to its plane $(I_z)$ is the sum of

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$ \frac{M}{12}(l^2 + b^2) $

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(A) According to the perpendicular axis theorem,the moment of inertia of a planar body about an axis perpendicular to its plane $(I_z)$ is the sum of the moments of inertia about two mutually perpendicular axes in its plane ($I_x$ and $I_y$) passing through the same point.For a rectangular plate of mass $M$,length $l$,and breadth $b$:The moment of inertia about an axis passing through the center and parallel to the breadth is $I_x = \frac{Ml^2}{12}$.The moment of inertia about an axis passing through the center and parallel to the length is $I_y = \frac{Mb^2}{12}$.By the perpendicular axis theorem,$I_z = I_x + I_y$.Therefore,$I_z = \frac{Ml^2}{12} + \frac{Mb^2}{12} = \frac{M}{12}(l^2 + b^2)$.

The moment of inertia of a rectangular plate of mass $M$,length $l$,and breadth $b$ about an axis perpendicular to its plane and passing through its center is:

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