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(D) The rate of heat flow $(H)$ through a rod is given by the formula $H = \frac{KA \Delta T}{L}$,where $K$ is the thermal conductivity,$A$ is the cro

Vedclass · Accepted Answer

$1:8$

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(D) The rate of heat flow $(H)$ through a rod is given by the formula $H = \frac{KA \Delta T}{L}$,where $K$ is the thermal conductivity,$A$ is the cross-sectional area,$\Delta T$ is the temperature difference,and $L$ is the length of the rod.Since the material is the same,$K$ is constant. Given that $\Delta T$ is also the same,we have $H \propto \frac{A}{L}$.The area $A = \pi r^2 = \pi (d/2)^2$,so $A \propto d^2$.Thus,the ratio of heat flow is $\frac{H_1}{H_2} = \left( \frac{d_1}{d_2} ight)^2 	imes \left( \frac{L_2}{L_1} ight)$.Given $\frac{d_1}{d_2} = \frac{1}{2}$ and $\frac{L_1}{L_2} = \frac{2}{1}$,we substitute these values:$\frac{H_1}{H_2} = \left( \frac{1}{2} ight)^2 	imes \left( \frac{1}{2} ight) = \frac{1}{4} 	imes \frac{1}{2} = \frac{1}{8}$.Therefore,the ratio is $1:8$.

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

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