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Question

The ratio of the areas of cross-section of two rods of different materials is 1:2, and the ratio of the thermal conductivities of their materials is 4:3. On keeping equal temperature difference between the ends of these rods, the rate of conduction of heat are equal. The ratio of the lengths of the rods is

A
2:3
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B
2:4
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C
4:2
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D
4:5
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Solution

The correct option is A 2:3
Given,
k1k2=1:2

A1A2=4:3

dQ1dt=dQ2dt

ΔT2=ΔT2

Now,

k1A1ΔT1l1=k2A2ΔT2l2
l1l2=k1A1k2A2=k1k2×A1A2

l1l2=23

Hence option A is the correct answer.

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