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Question

Two conductors of the same material have their diameters in the ratio $$1:2$$ and their lengths in the ratio $$2:1$$. If the temperature difference between their ends is same, then the ratio of amounts of heat conducted per second through them will be:


A
4:1
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B
1:4
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C
8:1
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D
1:8
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Solution

The correct option is D $$1:8$$
The rate of heat conduction is given by the formula 

$$\dfrac { dQ }{ dt } =\dfrac { kA }{ l } \Delta T$$

Since $$\Delta T$$ is same in both the cases, the ratio is ,
$$R=\dfrac { { A }_{ 1 } }{ { A }_{ 2 } } \dfrac { { l }_{ 2 } }{ { l }_{ 1 } } $$

$$R=\dfrac { { d }_{ 1 }^{ 2 } }{ { d }_{ 2 }^{ 2 } } \dfrac { { l }_{ 2 } }{ { l }_{ 1 } } =\dfrac { 1 }{ 4 } \times \dfrac { 1 }{ 2 } =\dfrac { 1 }{ 8 } $$

Physics

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