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QPages 11-12: Q9: HC Verma: Concepts of Physics - Volume 2 Heat and Temperature Pages 11-12: Q9 Solution: If the temperature of a uniform rod is slightly increased by ,…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students frequently treat thermal expansion as a uniform scaling of all dimensions and therefore multiply the original moment of inertia by $(1+\alpha\Delta t)$, forgetting that for an axis parallel to the rod the perpendicular distance $d$ to the axis does not change and the mass stays constant; consequently $I=Md^2$ remains unchanged (zero if the axis coincides with the rod).

If the temperature of a uniform rod is slightly increased by Δt\Delta t, its moment of inertia II about a line parallel to itself will increase by

Multiple Choice Options

  • A zero
  • B αIΔt\alpha I \Delta t
  • C 2αIΔt2\alpha I \Delta t
  • D 3αIΔt3\alpha I \Delta t

Step-by-Step Verified Solution

**Answer:** (a) zero. **Step-by-Step Explanation:** For a line parallel to the rod (passing through the rod), the moment of inertia is zero if the line coincides with the rod. If the line is parallel to the rod but displaced, the moment of inertia depends on the perpendicular distance, which does not change with temperature. Hence, the moment of inertia about a parallel line does not change.

All Questions in this Chapter

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