Question

Two cylindrical rods of the same material have the same temperature difference between their ends. The ratio of the rates of flow of heat through them is 1 : 8. The radii of the rods are in the ratio 1 : 2. What is the ratio of their lengths?

• A. 2 : 1
• B. 4 : 1
• C. 1 : 8
• D. 1 : 32

Answer 1

The correct option is A 2 : 1

$\frac{dQ}{dt}=\frac{kA\Delta \theta }{l}\Rightarrow H\alpha \frac{r^2}{l}$
$\therefore \frac{H_1}{H_2}=\frac{1}{8}=(\frac{1}{2}{)}^2\times \frac{l_2}{l_1}$
$\frac{l_2}{l_1}=\frac{1}{2}$
$\therefore l_1:l_2=2:1$