Question

The ratio of the diameters of two metallic rods of the same material is $2:1$ and their lengths are in the ratio $1:4$. If the temperature difference between them are equal, the rate of flow of heat in them will be in the ratio of

• A. $2:1$
• B. $4:1$
• C. $8:1$
• D. $16:1$

Answer 1

Answer: (D)

$16:1$

$\frac{Q}{t}=\frac{KA\left(\Delta \theta \right)}{l}⟹\frac{Q}{t}\propto \frac{A}{l}\propto \frac{r^2}{l}$
$\Rightarrow \frac{(Q/t{)}_1}{(Q/t{)}_2}=(\frac{r_1}{r_2}{)}^2\times \frac{l_2}{l_1}=(\frac{2}{1}{)}^2\times \frac{4}{1}=\frac{16}{1}$