Question

The heat is flowing through two cylindrical rods of same material. The diameters of the rods are in the ratio 1:2 and their lengths are in the ratio 2 : 1. If the temperature difference between their ends is the same, the ratio of rate of flow of heat through them will be

• A. 1 : 4
• B. 1 : 2
• C. 1 : 8
• D. 1 : 3

Answer 1

Answer: (C)

$ H=\frac{KA\Delta \theta }{l} $ or
$ H\propto \frac{{{r}^{2}}}{l} $
so, $ \frac{{{H}_{1}}}{{{H}_{2}}}={{\left( \frac{{{r}_{1}}}{{{r}_{2}}} \right)}^{2}}\left( \frac{{{I}_{2}}}{{{I}_{1}}} \right) $
$ ={{\left( \frac{1}{2} \right)}^{2}}\left( \frac{1}{2} \right) $
$ =\frac{1}{8} $
$ \Rightarrow $ $ {{H}_{1}}:{{H}_{2}}=1:8 $