Radius Of Gyration
A rigid body of mass 8 kg has a moment of inertia of 32 kg·m² about a particular axis of rotation. What is the radius of gyration of this body about that same axis?
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About This Question
- Subject
- physics
- Chapter
- rotational motion
- Topic
- radius of gyration
- Difficulty
- Medium
- Year
- 2025
Solution
Correct Answer:
2 m
As described in NCERT Class 11, Chapter 7 (System of Particles and Rotational Motion), the radius of gyration k is defined through the relation I = Mk², where it represents the single distance from the axis at which the entire mass of the body could be imagined to be concentrated to give the same moment of inertia. It is a convenient effective length that captures, in one number, how the mass of an arbitrarily shaped body is spread about a chosen axis, and it allows different bodies to be compared on equal footing. Rearranging the defining relation to solve for k gives k = √(I/M) = √(32/8) = √4 = 2 m. The option 4 m results from forgetting to take the square root after dividing the inertia by the mass. The option 0.5 m inverts the ratio inside the square root. The option 16 m comes from squaring the ratio rather than taking its root. A sanity check confirms that k carries units of metres, since √(kg·m²/kg) = √(m²) = m, and a radius of gyration of 2 m is fully consistent with the given moment of inertia of 32 kg·m² and mass of 8 kg.
This medium difficulty physics question is from the chapter rotational motion, covering the topic of radius of gyration. It appeared in the 2025 exam.
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