Question:
If the moment of inertia of a circular disc about its central axis is I, then that for the same disc about its diameter is
If the moment of inertia of a circular disc about its central axis is I, then that for the same disc about its diameter is
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For a disc, the moment of inertia about a diameter is half the moment of inertia about the central perpendicular axis.
Updated On: Apr 24, 2026
- I
- 2I
- 4I
- I/2
- I/4
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The Correct Option is D
Solution and Explanation
Step 1: Understanding the Concept:
The moment of inertia of a disc depends on the axis of rotation. There is a known relationship between the moment of inertia about the central (perpendicular) axis and about a diameter.
Step 2: Detailed Explanation:
Let \(M\) be the mass and \(R\) be the radius of the disc. Moment of inertia about the central axis (perpendicular to the plane through the center), \(I_{axis} = \frac{1}{2} M R^2\). Moment of inertia about any diameter (in the plane of the disc), \(I_{dia} = \frac{1}{4} M R^2\). Therefore, \(I_{dia} = \frac{1}{2} I_{axis}\). Given \(I_{axis} = I\), then \(I_{dia} = I/2\).
Step 3: Final Answer:
The moment of inertia about a diameter is \(I/2\).
The moment of inertia of a disc depends on the axis of rotation. There is a known relationship between the moment of inertia about the central (perpendicular) axis and about a diameter.
Step 2: Detailed Explanation:
Let \(M\) be the mass and \(R\) be the radius of the disc. Moment of inertia about the central axis (perpendicular to the plane through the center), \(I_{axis} = \frac{1}{2} M R^2\). Moment of inertia about any diameter (in the plane of the disc), \(I_{dia} = \frac{1}{4} M R^2\). Therefore, \(I_{dia} = \frac{1}{2} I_{axis}\). Given \(I_{axis} = I\), then \(I_{dia} = I/2\).
Step 3: Final Answer:
The moment of inertia about a diameter is \(I/2\).
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