Question:
Two rods (one semi-circular and other straight) of same material and cross-section are joined. The ratio of heat transferred through semi-circular rod to straight rod is
graphics[width=0.45\linewidth]{PHYSICS/QP21.png}
Two rods (one semi-circular and other straight) of same material and cross-section are joined. The ratio of heat transferred through semi-circular rod to straight rod is
graphics[width=0.45\linewidth]{PHYSICS/QP21.png}
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Heat conduction inversely depends on length when other factors are same.
Updated On: Apr 23, 2026
- \(2:\pi\)
- \(1:2\)
- \(\pi:2\)
- \(3:2\)
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The Correct Option is A
Solution and Explanation
Concept:
Heat conduction:
\[
Q = \frac{kA\Delta T}{L}t
\Rightarrow Q \propto \frac{1}{L}
\]
Step 1: Lengths
Straight rod: \[ L_1 = AB = 2r \] Semi-circular rod: \[ L_2 = \pi r \]
Step 2: Heat ratio
\[ \frac{Q_{\text{semi}}}{Q_{\text{straight}}} = \frac{1/L_2}{1/L_1} = \frac{L_1}{L_2} = \frac{2r}{\pi r} = \frac{2}{\pi} \] Conclusion: \[ 2:\pi \]
Step 1: Lengths
Straight rod: \[ L_1 = AB = 2r \] Semi-circular rod: \[ L_2 = \pi r \]
Step 2: Heat ratio
\[ \frac{Q_{\text{semi}}}{Q_{\text{straight}}} = \frac{1/L_2}{1/L_1} = \frac{L_1}{L_2} = \frac{2r}{\pi r} = \frac{2}{\pi} \] Conclusion: \[ 2:\pi \]
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