ABC is a triangular plate of uniform thicknes | vedclass

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(C) The moment of inertia of a body about an axis is given by $I = MK^2$,where $M$ is the mass and $K$ is the radius of gyration. The radius of gyrati

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$I_{BC} > I_{AB}$

Vedclass · Answer

(C) The moment of inertia of a body about an axis is given by $I = MK^2$,where $M$ is the mass and $K$ is the radius of gyration. The radius of gyration $K$ depends on the distribution of mass relative to the axis of rotation. The farther the mass is distributed from the axis,the larger the radius of gyration.In the given right-angled triangle $ABC$ with sides $AB=4$,$BC=3$,and $AC=5$:$1$. For axis $AB$,the mass is distributed within a distance of $3$ units.$2$. For axis $BC$,the mass is distributed within a distance of $4$ units.$3$. For axis $AC$,the mass is distributed within a smaller perpendicular distance compared to the other two axes.Since the mass is spread further away from the axis $BC$ compared to axis $AB$,the radius of gyration $K_{BC} > K_{AB}$.Consequently,$I_{BC} > I_{AB} > I_{CA}$.Therefore,the correct relation is $I_{BC} > I_{AB}$.

$ABC$ is a triangular plate of uniform thickness. Its sides are in the ratio as shown in the figure. Let $I_{AB}$,$I_{BC}$,and $I_{CA}$ be the moments of inertia of the plate about the sides $AB$,$BC$,and $CA$ respectively. Which of the following relations is true for this arrangement?

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