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
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$\frac{Q}{t} = \frac{KA \Delta \theta}{l}$ ⇒ ⇒ $\frac{Q}{t} \propto \frac{A}{l} \propto \frac{d^{2}}{l}$ (d = Diameter of rod)
⇒ ⇒ $\frac{(Q/t)_1}{(Q/t)_2} = \left(\frac{d_1}{d_2}\right)^2 \times \frac{l_2}{l_1} = \left(\frac{1}{2}\right)^2 \times \left(\frac{1}{2}\right) = \frac{1}{8}$
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