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MHT CET 2024 (16 May, Shift 1) · Moment of Inertia & Radius of Gyration

Moment of Inertia & Radius of Gyration question from MHT CET 2024 (16 May, Shift 1)

Q75MHT CET 2024 · 16 MAY · SHIFT 1Medium

Moment of Inertia & Radius of Gyration

Two spheres of equal masses, one of which is a thin spherical shell and the other solid sphere, have the same moment of inertia about their respective diameters. The ratio of their radii is

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Answer: (b)

  1. Shell: I=23MR12I = \frac{2}{3}MR_1^2; solid sphere: I=25MR22I = \frac{2}{5}MR_2^2.
  2. 23R12=25R22⇒R12R22=35\frac{2}{3}R_1^2 = \frac{2}{5}R_2^2 \Rightarrow \frac{R_1^2}{R_2^2} = \frac{3}{5}
  3. So the answer is (b) 3:5\sqrt{3} : \sqrt{5}.
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