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 :
Key Idea: Heat conduction through \[a\] rod is rate of change of heat \[\left( \frac{\Delta Q}{\Delta t} \right).\] \[\therefore \] \[H=\frac{\Delta Q}{\Delta t}=KA\left( \frac{{{T}_{1}}-{{T}_{2}}}{l} \right)\] \[\Rightarrow \] \[H\propto \frac{{{r}^{2}}}{l}\] ?(i) (a) When \[r=2{{r}_{0}},\]\[l=2{{l}_{0}}\] \[H\propto \frac{{{(2{{r}_{0}})}^{2}}}{2{{l}_{0}}}\] \[\Rightarrow \] \[H\propto \frac{2r_{0}^{2}}{{{l}_{0}}}\] (b) When \[r=2{{r}_{0}},\,\,l={{l}_{0}}\] \[H\propto \frac{{{(2{{r}_{0}})}^{2}}}{{{l}_{0}}}\] \[\Rightarrow \] \[H\propto \frac{4r_{0}^{2}}{{{l}_{0}}}\] (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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