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MHT CET 2023 (12 May, Shift 2) · Moment of Inertia & Radius of Gyration

Moment of Inertia & Radius of Gyration question from MHT CET 2023 (12 May, Shift 2)

Q103MHT CET 2023 · 12 MAY · SHIFT 2Medium

Moment of Inertia & Radius of Gyration

A thin wire of length ' $L$ ' and uniform linear mass density ' $m$ ' is bent into a circular coil. The moment of inertia of this coil about tangential axis and in plane of the coil is

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Answer: (b)

Mass $M = mL$ , radius $R = \frac{L}{2\pi}$ .
Tangent in the plane: $I = \frac{MR^2}{2} + MR^2 = \frac{3}{2}MR^2$ .
$I = \frac{3}{2}mL\cdot\frac{L^2}{4\pi^2} = \frac{3mL^3}{8\pi^2}$
So the answer is (b) $\frac{3mL^3}{8\pi^2}$ .

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