Moment Of Inertia
What is the moment of inertia of a uniform rod of mass M and length L about an axis perpendicular to it through its center?
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About This Question
- Subject
- physics
- Chapter
- rotational motion
- Topic
- moment of inertia
- Difficulty
- Easy
- Year
- 2025
Solution
Correct Answer:
ML²/12
- Definition: Moment of inertia (I) represents a body's resistance to angular acceleration about a specific axis.
- Derivation Logic: Imagine the rod on the X-axis from −L/2 to +L/2. Mass of an element dx is dm=(M/L)dx.
- Integral: I=∫r2dm=∫−L/2L/2x2LMdx.
- Result: LM[3x3]−L/2L/2=LM(24L3−(−24L3))=12ML2.
- Note: If the axis passes through one end, the limit changes to 0 to L, giving ML2/3.
This easy difficulty physics question is from the chapter rotational motion, covering the topic of moment of inertia. It appeared in the 2025 exam.
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