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NEET 2026 · Moment of Inertia & Radius of Gyration

Moment of Inertia & Radius of Gyration question from NEET 2026

Q29NEET 2026Medium

Moment of Inertia & Radius of Gyration

A thin wire of length ' LL ' and linear mass density ' mm ' is bent into a circular ring (in x−yx-y plane) with centre ' CC ' as shown in figure. The moment of inertia of the ring about an axis yy′yy' will be:

Figure

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Answer: (b)

  1. Mass M=mLM = mL, radius R=L2πR = \frac{L}{2\pi}.
  2. yy′yy' touches the ring and lies in its plane (tangent): I=MR22+MR2=32MR2I = \frac{MR^2}{2} + MR^2 = \frac{3}{2}MR^2.
  3. I=32mL⋅L24π2=3mL38π2I = \frac{3}{2}mL\cdot\frac{L^2}{4\pi^2} = \frac{3mL^3}{8\pi^2}
  4. So the answer is (b) 3mL38π2\frac{3mL^3}{8\pi^2}.
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