A) 4 : 1
B) 1 : 4
C) 8 : 1
D) 1 : 8
Correct Answer: D
Solution :
The resistance of conductor \[R=\frac{\rho l}{A}=\frac{\rho l}{\pi {{r}^{2}}}\] or \[R\propto \frac{l}{{{r}^{2}}}\] \[\therefore \] \[\frac{{{R}_{1}}}{{{R}_{2}}}=\frac{{{l}_{1}}}{{{l}_{2}}}\times \frac{r_{2}^{2}}{r_{1}^{2}}\] \[=\frac{2}{1}\times {{\left( \frac{2}{1} \right)}^{2}}=\frac{8}{1}\] Thermal potentials between the ends of the rods are same. So, heat conducted per second \[H=\frac{Q}{t}\propto \frac{1}{R}\] \[\therefore \] \[\frac{{{H}_{1}}}{{{H}_{2}}}=\frac{{{R}_{2}}}{{{R}_{1}}}=\frac{1}{8}=1:8\]
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