Heat is flowing through two cylindrical rods of same material. diameters of rods are in ratio 1 : 2

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10-2.Transmission of Heat

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Heat is flowing through two cylindrical rods of the 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, then the ratio of the amounts of heat conducted through per unit time will be

A

$1:1$

B

$2:1$

C

$1:4$

D

$1:8$

Solution

Ratio of diameters of rod: $1: 2$ and ratio of their lengths $2: 1$

The rate of flow of heat, $(R)$

$=\frac{K A \Delta T}{1} \propto \frac{A}{1}$

Therefore $\frac{R_{1}}{R_{2}}=\frac{A_{1}}{A_{2}} \times \frac{l_{2}}{l_{1}}=$

$\left(\frac{1}{2}\right)^{2} \times \frac{1}{2}=\frac{1}{8}$

or $\quad R_{1}: R_{2}=1: 8$

Standard 11

Physics

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