Which of the following circular rods (given r | vedclass

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(B) The rate of heat conduction $H$ through a rod is given by the formula $H = \frac{kA \Delta T}{l}$,where $k$ is the thermal conductivity,$A$ is the

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$r = 2r_0; l = l_0$

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(B) The rate of heat conduction $H$ 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.Since the material is the same,$k$ is constant. Since the temperature difference $\Delta T$ is the same,$H \propto \frac{A}{l}$.For a circular rod,the cross-sectional area $A = \pi r^2$,so $H \propto \frac{r^2}{l}$.Evaluating the ratio $\frac{r^2}{l}$ for each option:$(a) \frac{(2r_0)^2}{2l_0} = \frac{4r_0^2}{2l_0} = 2 \frac{r_0^2}{l_0}$$(b) \frac{(2r_0)^2}{l_0} = \frac{4r_0^2}{l_0} = 4 \frac{r_0^2}{l_0}$$(c) \frac{r_0^2}{l_0} = 1 \frac{r_0^2}{l_0}$$(d) \frac{r_0^2}{2l_0} = 0.5 \frac{r_0^2}{l_0}$Comparing these values,option $(b)$ has the highest ratio,meaning it conducts the most heat.

Which of the following circular rods (given radius $r$ and length $l$),each made of the same material and whose ends are maintained at the same temperature difference,will conduct the most heat?

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