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Which of the following circular rods (given radius r and length l), each made of the same material and whose ends are maintained at the same temperature will conduct most heat?

1. r = r₀; l = l₀
2. r = 2r₀; l = l₀
3. r = r₀; l = 2l₀
4. r = 2r₀; l = 2l₀

Correct answer: r = 2r₀; l = l₀

Solution

The rate of heat conduction is proportional to the cross-sectional area (∝ r²) and inversely proportional to the length (∝ 1/l). Option B has the largest radius (2r₀) and the smallest length (l₀), maximizing heat conduction.

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