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TS EAMCET · Physics · Rotational Motion

Two solid spheres \(A\) and \(B\) each of radius \(R\) are made of materials of densities \(\rho_A\) and \(\rho_B\) respectively. Their moments of inertia about a diameter are \(I_A\) and \(I_B\) respectively. The value of \(\frac{I_A}{I_B}\) is

  1. A \(\sqrt{\frac{\rho_A}{\rho_B}}\)
  2. B \(\sqrt{\frac{\rho_B}{\rho_A}}\)
  3. C \(\frac{\rho_A}{\rho_B}\)
  4. D \(\frac{\rho_B}{\rho_A}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\frac{\rho_A}{\rho_B}\)

Step-by-step Solution

Detailed explanation

Moment of inertia \(\begin{aligned} I & =\frac{2}{3} M R^2 \\ \therefore \quad \frac{I_A}{I_B} & =\frac{\frac{2}{5} M_A R^2}{\frac{2}{5} M_B R^2}=\frac{\frac{4}{3} \pi R^3 \rho_A}{\frac{4}{3} \pi R^3 \rho_B}=\frac{\rho_A}{\rho_B}\end{aligned}\)
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