Question

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

• A. 2:1
• B. 8:1
• C. 1:1
• D. 1:8

Answer 1

Answer: (D)

1:8

Answer 2

Ratio of diameters of rod = 1 : 2 and ratio of their lengths 2:1.
The rate of flow of heat, $(R) = \frac{ KA \Delta T}{l} \propto \frac{A}{l}$
$\therefore \, \, \, \, \, \frac{R_1}{R_2}= \frac{ A_1}{A_2} \times \frac{l_2}{l_1} = \bigg( \frac{1}{2} \bigg)^2 \times \frac{1}{2} = \frac{1}{8}$
or $R_1 : R_2 = 1:8$
Therefore, the correct option is (D) : 1:8