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JEE Main 2019 (12 Jan, Shift 1) · Moment of Inertia & Radius of Gyration

Moment of Inertia & Radius of Gyration question from JEE Main 2019 (12 Jan, Shift 1)

Q159JEE Main 2019 · 12 JAN · SHIFT 1Medium

Moment of Inertia & Radius of Gyration

Let the moment of inertia of a hollow cylinder of length 30 cm (inner radius 10 cm and outer radius 20 cm), about its axis be I. The radius of a thin cylinder of the same mass such that its moment of inertia about its axis is also I, is:

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Answer: (a)

Hollow cylinder: $I = \frac{M}{2}(R_1^2 + R_2^2) = \frac{M}{2}(100 + 400) = 250M$ (cm units).
Thin cylinder: $I = MR^2$ .
$R^2 = 250 \Rightarrow R \approx 15.8\text{ cm}$
So the answer is (a) 16 cm.

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