Topic: Moment of inertia, radius of gyration, MI of simple objects· Rotational Motion

The ratio of radius of gyration of a solid sphere of mass M and radius R about its own axis to the radius of gyration of the thin hollow sphere of same mass and radius about its axis is :

1. 5 : 2

2. 3 : 5

3. 5 : 3

4. 2 : 5

Doubtly Asked 30 Oct 2026 NEET UG 2023 neet Save WhatsApp Report

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Answer: Dropped in the official answer key: full marks to every candidate

Radius of gyration is \(k=\sqrt{I/M}\).

Solid sphere about its axis: \(I=\tfrac25MR^2\), so \(k_1^2=\tfrac25R^2\).
Thin hollow sphere: \(I=\tfrac23MR^2\), so \(k_2^2=\tfrac23R^2\).

\(\dfrac{k_1}{k_2}=\sqrt{\dfrac{2/5}{2/3}}=\sqrt{\dfrac35}\). The ratio 3 : 5 given in an option is the ratio of \(k^2\), not of \(k\). None of the options equals \(\sqrt3:\sqrt5\), so this question was dropped from the official key.

Doubtly AI · 30 Oct 2026 AI-generated · not yet verified Report

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The ratio of radius of gyration of a solid sphere of mass M and radius R about its own axis to the radius of gyration of the thin hollow sphere of same mass and radius about its axis is :

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