A) 3 : 2 : 1
B) 1 : 2 : 3
C) 27 : 6 : 1
D) 1 : 6 : 27
Correct Answer: C
Solution :
Resistance of wire \[R=\frac{\rho l}{A}\] or \[R\propto \frac{{{l}^{2}}}{Al}\] or \[R\propto \frac{{{l}^{2}}}{V}\] or \[R\propto \frac{{{l}^{2}}d}{m}\] (where\[d\]is density and \[m\] is mass) or \[R\propto \frac{{{l}^{2}}}{m}\] Here, \[{{l}_{1}}:{{l}_{2}}:{{l}_{3}}=3:2:1\] \[{{m}_{1}}:{{m}_{2}}:{{m}_{3}}=1:2:3\] \[\therefore \] \[{{R}_{1}}:{{R}_{2}}:{{R}_{3}}:\,\,:\,\frac{{{l}_{1}}^{2}}{{{m}_{1}}}:\frac{{{l}_{2}}^{2}}{{{m}_{2}}}:\frac{{{l}_{3}}^{2}}{{{m}_{3}}}\] or \[{{R}_{1}}:{{R}_{2}}:{{R}_{3}}:\,\,:\,\frac{9}{1}:\frac{4}{2}:\frac{1}{3}\] or \[{{R}_{1}}:{{R}_{2}}:{{R}_{3}}:\,\,:\,27:6:1\]
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