In a rectangle ABCD where BC = 2AB,the moment | vedclass

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(D) Let the length $AB = CD = a$ and the width $BC = AD = 2a$. The mass of the rectangle is $M$.For a rectangular lamina of sides $a$ and $b$,the mome

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$EG$

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(D) Let the length $AB = CD = a$ and the width $BC = AD = 2a$. The mass of the rectangle is $M$.For a rectangular lamina of sides $a$ and $b$,the moment of inertia about an axis passing through the center and parallel to side $b$ is $I = \frac{Ma^2}{12}$.$1$. For axis $EG$ (parallel to $BC$): The distance of mass distribution is along $AB$. Here,$I_{EG} = \frac{M(AB)^2}{12} = \frac{Ma^2}{12}$.$2$. For axis $HF$ (parallel to $AB$): The distance of mass distribution is along $BC$. Here,$I_{HF} = \frac{M(BC)^2}{12} = \frac{M(2a)^2}{12} = \frac{4Ma^2}{12} = \frac{Ma^2}{3}$.Comparing the two,$I_{EG} Since the moment of inertia is proportional to the square of the distance of the mass from the axis,the axis that passes through the center and is parallel to the longer side will have the minimum moment of inertia.Therefore,the moment of inertia is minimum about the axis $EG$.

In a rectangle $ABCD$ where $BC = 2AB$,the moment of inertia will be minimum about which axis?

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