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JEE Main 2021 (18 Mar, Shift 2) · Moment of Inertia & Radius of Gyration

Moment of Inertia & Radius of Gyration question from JEE Main 2021 (18 Mar, Shift 2)

Q137JEE Main 2021 · 18 MAR · SHIFT 2Medium

Moment of Inertia & Radius of Gyration

Consider a uniform wire of mass M and length L. It is bent into a semicircle. Its moment of inertia about a line perpendicular to the plane of the wire passing through the center is:

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Answer: (d)

  1. Semicircle: L=πR⇒R=LπL = \pi R \Rightarrow R = \frac{L}{\pi}.
  2. Every element is at distance RR from the axis: I=MR2I = MR^2.
  3. I=ML2π2I = \frac{ML^2}{\pi^2}
  4. So the answer is (d) ML2π2\frac{ML^2}{\pi^2}.
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