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NEET 2016 (Phase 1) · Moment of Inertia & Radius of Gyration

Moment of Inertia & Radius of Gyration question from NEET 2016 (Phase 1)

Q176NEET 2016 · PHASE 1Medium

Moment of Inertia & Radius of Gyration

From a disc of radius R and mass M, a circular hole of diameter R, whose rim passes through the centre is cut. What is the moment of inertia of the remaining part of the disc about a perpendicular axis, passing through the centre?

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Answer: (d)

  1. Hole radius R2\frac{R}{2}, mass M4\frac{M}{4}, centre at R2\frac{R}{2} from O.
  2. Ihole=12M4R24+M4R24=3MR232I_{hole} = \frac{1}{2}\frac{M}{4}\frac{R^2}{4} + \frac{M}{4}\frac{R^2}{4} = \frac{3MR^2}{32}
  3. I=MR22−3MR232=13MR232I = \frac{MR^2}{2} - \frac{3MR^2}{32} = \frac{13MR^2}{32}
  4. So the answer is (d).
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