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NEET 2004 (AIPMT) · Moment of Inertia & Radius of Gyration

Moment of Inertia & Radius of Gyration question from NEET 2004 (AIPMT)

Q196NEET 2004 · AIPMTMedium

Moment of Inertia & Radius of Gyration

The ratio of the radii of gyration of a circular disc about a tangential axis in the plane of the disc and of a circular ring of the same radius about a tangential axes in the plane of the ring is

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Answer: (c)

  1. Disc, tangent in its plane: K12=14R2+R2=54R2K_1^2 = \frac{1}{4}R^2 + R^2 = \frac{5}{4}R^2.
  2. Ring, tangent in its plane: K22=12R2+R2=32R2K_2^2 = \frac{1}{2}R^2 + R^2 = \frac{3}{2}R^2.
  3. K1K2=56\frac{K_1}{K_2} = \sqrt{\frac{5}{6}}
  4. So the answer is (c) 5:6\sqrt{5} : \sqrt{6}.
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