A) \[4\,{{Q}_{1}}\]
B) \[2\,{{Q}_{1}}\]
C) \[\frac{{{Q}_{1}}}{4}\]
D) \[\frac{{{Q}_{1}}}{2}\]
Correct Answer: B
Solution :
Rate of heat flow \[\left( \frac{Q}{t} \right)=\frac{k\pi {{r}^{2}}({{\theta }_{1}}-{{\theta }_{2}})}{L}\propto \frac{{{r}^{2}}}{L}\] \[\therefore \] \[\frac{{{Q}_{1}}}{{{Q}_{2}}}={{\left( \frac{{{r}_{1}}}{{{r}_{2}}} \right)}^{2}}\left( \frac{{{l}_{2}}}{{{l}_{1}}} \right)={{\left( \frac{1}{2} \right)}^{2}}\times \left( \frac{2}{1} \right)=\frac{1}{2}\] \[\Rightarrow \]\[{{Q}_{2}}=2{{Q}_{1}}\]
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