Q117 / 200 · NEET 2005 · Physics

Which of the following 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?

  • A
    $r=r_0 \quad l=l_0$
  • Correct answer
    B
    $r=2 r_0 \quad l=l_0$
  • C
    $r=r_0 \quad l=2 l_0$
  • D
    $r=2 r_0 \quad l=2 l_0$

Solution

Heat conducted $$ =\frac{K A\left(T_1-T_2\right) t}{l}=\frac{K \pi r^2\left(T_1-T_2\right) t}{l} $$ The rod with maximum ratio of $\frac{A}{l}$ will conduct most. Here the rod $r=2 r_0$ and $l=l_0$ will conduct most.

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

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