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MHT CET 2021 (22 Sep, Shift 2) · Moment of Inertia & Radius of Gyration

Moment of Inertia & Radius of Gyration question from MHT CET 2021 (22 Sep, Shift 2)

Q134MHT CET 2021 · 22 SEP · SHIFT 2Medium

Moment of Inertia & Radius of Gyration

Two rings of radius 'R' and 'nR' made of same material have the ratio of moment of inertia about an axis passing through its centre and perpendicular to the plane is $1 : 8$ . The value of ' $n$ ' is (mass per unit length $= \lambda$ )

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Answer: (a)

Ring: $I = (2\pi R\lambda)R^2 = 2\pi\lambda R^3 \propto R^3$ .
$\frac{R^3}{(nR)^3} = \frac{1}{8} \Rightarrow n^3 = 8$
So the answer is (a) $n = 2$ .

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