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A semicircular rod is joined at both ends to a straight rod made of the same material and having the same cross-sectional area; the straight rod is the diameter of the semicircle. The two junctions are kept at different fixed temperatures. In a given time, what is the ratio of heat conducted through a cross-section of the semicircular rod to that through the straight rod?

1. pi: 2
2. 2: pi
3. 1: pi
4. pi: 1

Correct answer: 2: pi

Solution

With the same dT, k and A, the heat current is inversely proportional to length; lengths are pi*r (semicircle) and 2r (straight), giving the ratio (1/(pi r)): (1/(2r)) = 2: pi.

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