Two solid spheres A and B, each of radius R, are made of materials of densities $ρ_{A}$ and $ρ_{B}$ respectively. Their moments of inertia about a diameter are $I_{A}$ and $I_{B}$ respectively. The ratio $I_{A} / I_{B}$ is

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$\frac{ρ_{B}}{ρ_{A}}$

$\sqrt{\frac{ρ_{B}}{ρ_{A}}}$

$\sqrt{\frac{ρ_{A}}{ρ_{B}}}$

$\frac{ρ_{A}}{ρ_{B}}$

answer is C.

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Detailed Solution

Mass of sphere $A, M_{A} = \frac{4}{3} π R^{3} ρ_{A}$ , mass of sphere B,
$M_{B} = \frac{4}{3} π R^{3} ρ_{B} .$

Now, $I_{A} = \frac{2}{5} M_{A} R^{2}$ and $I_{B} = \frac{2}{5} M_{B} R^{2} .$ Therefore,
$\frac{I_{A}}{I_{B}} = \frac{M_{A}}{M_{B}} = \frac{ρ_{A}}{ρ_{B}}$

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