Ratio of Radii of Spheres – Rankers Physics
Topic: Rotational Motion
Subtopic: Moment of Inertia

Ratio of Radii of Spheres

A uniform solid sphere and a uniform hollow sphere of the same mass have the same moment of inertia about their diameters. Then the radii of solid and hollow sphere are in the ratio
\(\sqrt{\frac{3}{5}}\)
\(\sqrt{\frac{5}{3}}\)
\(\frac{3}{5}\)
\(\frac{5}{3}\)

Solution:

We are given \(I_{\text{solid}} = I_{\text{hollow}} ⇒ \frac{2}{5}M R_s^2 = \frac{2}{3}M R_h^2\). Thus, \(\frac{R_s}{R_h} = \sqrt{\frac{5}{3}}\).

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