Q132 / 180 · KCET 2016 · Physics

Four rods with different radii \( r \) and length \( l \) are used to connect two heat reservoirs at different
temperature. Which one will conduct most heat?

  • A
    \( r=1 \mathrm{~cm}, l=1 \mathrm{~m} \)
  • B
    \( r=1 \mathrm{~cm}, l=\frac{1}{2} m \)
  • C
    \( r=2 \mathrm{~cm}, l=2 \mathrm{~m} \)
  • Correct answer
    D
    \( r=2 \mathrm{~cm}, l=\frac{1}{2} m \)

Solution

The amount of heat conducted depends on radii r andlength I as
\( Q \propto \frac{r^{2}}{l} \)
Thus, rod will conduct maximum for maximum r value and minimum I value,
Therefore, \( r=2 \mathrm{~cm} \) and \( l=\frac{1}{2} m \)

Hence, the correct answer is option: 'D'.

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