A) \[r=2{{r}_{0}};\,\,l=2{{l}_{0}}\]
B) \[r=2{{r}_{0}};l={{l}_{0}}\]
C) \[r={{r}_{0}};l={{l}_{0}}\]
D) \[r={{r}_{0}};l=2{{l}_{0}}\]
Correct Answer: B
Solution :
Heat conduction through a rod is given by \[H=\frac{\Delta Q}{\Delta t}=KA\left( \frac{{{T}_{1}}-{{T}_{2}}}{l} \right)\] \[\Rightarrow \] \[H\propto \frac{{{r}^{2}}}{l}\] ?(i) (a) When \[r=2{{r}_{0}};\,\,l=2{{l}_{0}}\] \[H\propto \frac{{{(2{{r}_{0}})}^{2}}}{2{{l}_{0}}}\] \[\Rightarrow \] \[H\propto \frac{2{{r}_{0}}^{2}}{2{{l}_{0}}}\] (b) When \[r=2{{r}_{0}};\]\[l={{l}_{0}}\] \[H\propto \frac{{{(2{{r}_{0}})}^{2}}}{{{l}_{0}}}\] \[\Rightarrow \] \[H\propto \frac{4{{r}_{0}}^{2}}{{{l}_{0}}}\] (c) When \[r={{r}_{0}};\] \[l={{l}_{0}}\] \[H\propto \frac{{{r}_{0}}^{2}}{{{l}_{0}}}\] (d) When \[r={{r}_{0}};\,\,l=2{{l}_{0}}\] \[H\propto \frac{{{r}_{0}}^{2}}{2{{l}_{0}}}\] It is obvious that heat conduction will be more in case (b).
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