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 : 1
• B. 2 : 1
• C. 1 : 4
• D. 1 : 8

Answer 1

The correct option is D

1 : 8

$\frac{Q}{t}=\frac{KA△\theta }{l}\Rightarrow \frac{Q}{T}\propto \frac{A}{l}\propto \frac{d^2}{l}$

( d = Diameter of rod )

$\Rightarrow \frac{(Q/t{)}_1}{(Q/t{)}_2}={\left(\frac{d_1}{d_2}\right)}^2\times \frac{l_2}{l_1}={\left(\frac{1}{2}\right)}^2\times \left(\frac{1}{2}\right)=\frac{1}{8}$