Solution:
The rate of heat conduction is $H = \frac{KA\Delta T}{l} = \frac{K(\pi r^2)\Delta T}{l}$. Since material and $\Delta T$ are same, $H \propto \frac{r^2}{l}$. This ratio is maximum for $r = 2r_0$ and $l = l_0$ (ratio $\propto 4$).
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? (2005)
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