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QPages 98-102: Q17: HC Verma: Concepts of Physics - Volume 2 Heat Transfer Pages 98-102: Q17 Solution: A semicircular rod is joined at its end to a straight rod of…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students frequently mistake the length of the semicircular rod for the diameter ($2r$) instead of the arc length ($\pi r$). Always calculate the actual path length for heat conduction, which is the circumference of the semicircle ($\pi r$), not the straight-line distance between endpoints.

A semicircular rod is joined at its end to a straight rod of the same material and the same cross-sectional area. The straight rod forms a diameter of the other rod. The junctions are maintained at different temperatures. Find the ratio of the heat transferred through a cross section of the semicircular rod to the heat transferred through a cross section of the straight rod in a given time.

Step-by-Step Verified Solution

**Answer:** Ratio = 2/�. **Step-BY-Step Explanation:** For semicircular rod (length = �r): q_ = KA _T/(�r). For straight rod (length = 2r): q_ = KA _T/(2r).
q1q2=2rπr=2π\frac{q_1}{q_2} = \frac{2r}{\pi r} = \frac{2}{\pi}
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All Questions in this Chapter

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