Q151 / 160 · AP EAMCET 2012 · Physics

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

  • A
    $\sqrt{\frac{\rho_A}{\rho_B}}$
  • B
    $\sqrt{\frac{\rho_B}{\rho_A}}$
  • Correct answer
    C
    $\frac{\rho_A}{\rho_B}$
  • D
    $\frac{\rho_B}{\rho_A}$

Solution

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

Hence, the correct answer is option: 'C'.

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