A) \[1:2\]
B) \[2:1\]
C) \[1:8\]
D) \[8:1\]
Correct Answer: D
Solution :
\[{{R}_{1}}=\rho \frac{{{l}_{1}}}{{{A}_{1}}}\] and \[{{R}_{2}}=\rho \frac{{{l}_{2}}}{{{A}_{2}}}\]Þ \[\,\frac{{{R}_{1}}}{{{R}_{2}}}=\frac{{{l}_{1}}}{{{l}_{2}}}.\frac{{{A}_{2}}}{{{A}_{1}}}=\frac{{{l}_{1}}}{{{l}_{2}}}{{\left( \frac{{{r}_{2}}}{{{r}_{1}}} \right)}^{2}}\] Given \[\frac{{{l}_{1}}}{{{l}_{2}}}=\frac{1}{2}\] and \[\frac{{{r}_{1}}}{{{r}_{2}}}=\frac{2}{1}\] or \[\frac{{{r}_{2}}}{{{r}_{1}}}=\frac{1}{2}\]Þ \[\frac{{{R}_{1}}}{{{R}_{2}}}=\frac{1}{8}\] \[\therefore \] Ratio of heats \[\frac{{{H}_{1}}}{{{H}_{2}}}=\frac{{{V}^{2}}/{{R}_{1}}}{{{V}^{2}}/{{R}_{2}}}=\frac{{{R}_{2}}}{{{R}_{1}}}=\frac{8}{1}\]
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