Radius Of Gyration
A rigid body of mass 4 kg is found to have a moment of inertia of 16 kg m^2 about a particular axis of rotation. What is the radius of gyration of this body about the same axis?
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About This Question
- Subject
- physics
- Chapter
- rotational motion
- Topic
- radius of gyration
- Difficulty
- Easy
- Year
- 2025
Solution
Correct Answer:
2 m
The radius of gyration k is defined so that the entire mass of a body, if placed at distance k from the axis, would reproduce the actual moment of inertia, through the relation I=Mk2. Solving for k gives k=MI. Substituting the given values, k=416=4=2 m. The value 4 m comes from dividing I by M but forgetting to take the square root. The value 8 m wrongly multiplies rather than divides and also skips the square root. The value 1 m takes an incorrect square root of the ratio. This is the NCERT definition that lets a complicated mass distribution be summarised by a single effective distance from the axis. As a unit and magnitude check, kg m2/kg=m2=m, so the result correctly carries units of length, and a radius of gyration of 2 m is physically reasonable for the stated inertia and mass.
This easy 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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