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MHT CET 2024 (4 May, Shift 2) · Moment of Inertia & Radius of Gyration

Moment of Inertia & Radius of Gyration question from MHT CET 2024 (4 May, Shift 2)

Q82MHT CET 2024 · 4 MAY · SHIFT 2Medium

Moment of Inertia & Radius of Gyration

Two solid spheres ( A and B) are made of metals having densities ρA\rho_A and ρB\rho_B respectively. If there masses are equal then ratio of their moments of inertia (IBIA)\left(\frac{I_B}{I_A}\right) about their respective diameter is

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Answer: (b)

  1. Equal mass: 43πR3ρ=\frac{4}{3}\pi R^3 \rho = constant, so R∝ρ−1/3R \propto \rho^{-1/3}.
  2. I=25MR2∝R2∝ρ−2/3I = \frac{2}{5}MR^2 \propto R^2 \propto \rho^{-2/3}
  3. IBIA=(ρAρB)2/3\frac{I_B}{I_A} = \left(\frac{\rho_A}{\rho_B}\right)^{2/3}
  4. So the answer is (b).
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