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MHT CET 2019 (2 May, Shift 1) · Moment of Inertia & Radius of Gyration

Moment of Inertia & Radius of Gyration question from MHT CET 2019 (2 May, Shift 1)

Q161MHT CET 2019 · 2 MAY · SHIFT 1Medium

Moment of Inertia & Radius of Gyration

A thin metal wire of length 'L' and uniform linear mass density 'ρ\rho' is bent into a circular coil with 'O' as centre. the moment of inertia of a coil about the axis XX' is

Figure

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Answer: (a)

  1. Mass M=ρLM = \rho L, radius R=L2πR = \frac{L}{2\pi}.
  2. XX′XX' is a tangent in the plane of the coil: I=32MR2I = \frac{3}{2}MR^2.
  3. I=32ρL⋅L24π2=3ρL38π2I = \frac{3}{2}\rho L\cdot\frac{L^2}{4\pi^2} = \frac{3\rho L^3}{8\pi^2}
  4. So the answer is (a) 3ρL38π2\frac{3\rho L^3}{8\pi^2}.
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