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(B) The rate of heat conduction $H$ through a cylindrical rod is given by the formula $H = \frac{KA \Delta T}{L}$,where $K$ is the thermal conductivit

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Length $1 \ m$,radius $2 \ cm$

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(B) The rate of heat conduction $H$ through a cylindrical 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 $A = \pi r^2$,the expression becomes $H = \frac{K \pi r^2 \Delta T}{L}$.Assuming the material $(K)$ and the temperature difference $(\Delta T)$ are the same for all rods,the heat conduction $H$ is proportional to $\frac{r^2}{L}$.Calculating the ratio $\frac{r^2}{L}$ for each option:$(a)$ $\frac{1^2}{1} = 1$$(b)$ $\frac{2^2}{1} = 4$$(c)$ $\frac{1^2}{2} = 0.5$$(d)$ $\frac{2^2}{2} = 2$Comparing these values,the ratio is maximum for option $(b)$. Therefore,the rod with length $1 \ m$ and radius $2 \ cm$ will conduct the most heat.

Which of the following cylindrical rods will conduct the most heat when their ends are maintained at the same steady temperatures?

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