Rankers Physics

Uncategorized: Practice Problem & Solution

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: (1995)
$2 : 1$
$8 : 1$
$1 : 1$
$1 : 8$

Solution Explained:

To solve this problem, we apply the core principles of Uncategorized. Understanding the underlying formula is key to arriving at the correct answer below:

Rate of heat flow $H = \frac{KA\Delta T}{L} \propto \frac{r^2}{L}$. Ratio $H_1 / H_2 = (r_1/r_2)^2 \times (L_2/L_1) = (1/2)^2 \times (1/2) = 1/4 \times 1/2 = 1/8$.

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