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
B
1:4
C
8:1
D
1:8

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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