Heat is flowing through two cylindrical rods of the 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, then the ratio of the amounts of heat conducted through per unit time will be
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Ratio of diameters of rod: $1: 2$ and ratio of their lengths $2: 1$
The rate of flow of heat, $(R)$
$=\frac{K A \Delta T}{1} \propto \frac{A}{1}$
Therefore $\frac{R_{1}}{R_{2}}=\frac{A_{1}}{A_{2}} \times \frac{l_{2}}{l_{1}}=$
$\left(\frac{1}{2}\right)^{2} \times \frac{1}{2}=\frac{1}{8}$
or $\quad R_{1}: R_{2}=1: 8$
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