The ABC is a triangular plate of uniform thickness. The sides are in… | NEET 1995 (AIPMT)

Q202NEET 1995 · AIPMTMedium

Moment of Inertia & Radius of Gyration

The $ABC$ is a triangular plate of uniform thickness. The sides are in the ratio shown in the figure. $I_{AB}, I_{BC}$ and $I_{CA}$ are the moments of inertia of the plate about $AB, BC$ and $CA$ respectively. Which one of the following relations is correct?

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Answer: (d)

For a triangular plate, $I$ about a side $= \frac{Mh^2}{6}$ , where $h$ is the height of the opposite vertex from that side.
Right angle at B: about AB, $h = BC = 3$ ; about BC, $h = AB = 4$ ; about CA, $h = \frac{3 \times 4}{5} = 2.4$ .
$I_{AB} \propto 9$ , $I_{BC} \propto 16$ , $I_{CA} \propto 5.76$ : mass lies farther from BC than from AB.
So the answer is (d) $I_{BC} > I_{AB}$ .

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