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TS EAMCET · Physics · Rotational Motion

Two solid spheres ( \(A\) and \(B\) ) are made of metals of different densities \(\rho_A\) and \(\rho_B\) respectively. If their masses are equal, the ratio of their moments of inertia \(\left(I_B / I_A\right)\) about their respective diameter is

  1. A \(\left(\frac{\rho_B}{\rho_A}\right)^{2 / 3}\)
  2. B \(\left(\frac{\rho_A}{\rho_B}\right)^{2 / 3}\)
  3. C \(\frac{\rho_A}{\rho_B}\)
  4. D \(\frac{\rho_B}{\rho_A}\)
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Correct Answer

(A) \(\left(\frac{\rho_B}{\rho_A}\right)^{2 / 3}\)

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Detailed explanation

As two solid spheres are equal in masses, so \(m_A=m_B\) \(\begin{aligned} \Rightarrow & \frac{4}{3} \pi R_A^3 \rho_A & =\frac{4}{3} \pi R_B^3 \rho_B \\ \Rightarrow & \frac{R_A}{R_B} & =\left(\frac{\rho_B}{\rho_A}\right)^{1 / 3}\end{aligned}\) The moment of inertia of sphere…
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