For a rectangle ABCD with BC = 2AB,about whic | vedclass

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(D) Let the mass of the rectangle be $M$. Let $AB = l$ and $BC = 2l$. The moment of inertia of a rectangle about an axis passing through its center an

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$EG$

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(D) Let the mass of the rectangle be $M$. Let $AB = l$ and $BC = 2l$. The moment of inertia of a rectangle about an axis passing through its center and parallel to its sides is given by $I = \frac{M d^2}{12}$,where $d$ is the side perpendicular to the axis. $1$. For axis $HF$ (parallel to $AB$): The perpendicular side is $BC = 2l$. So,$I_{HF} = \frac{M(2l)^2}{12} = \frac{4Ml^2}{12} = \frac{Ml^2}{3}$. $2$. For axis $EG$ (parallel to $BC$): The perpendicular side is $AB = l$. So,$I_{EG} = \frac{Ml^2}{12}$. Comparing the two,$I_{EG} Since $EG$ passes through the center and is parallel to the longer side,it results in the minimum moment of inertia among the given options.

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

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