A) \[1:3:5\]
B) \[5:3:1\]
C) \[\text{1}:15:125\]
D) \[125:15:1\]
Correct Answer: D
Solution :
As \[R=\frac{\rho l}{A}=\frac{\rho {{l}^{2}}}{A\,I}=\frac{\rho {{l}^{2}}}{V}=\frac{\rho {{l}^{2}}}{m/d}\] \[\Rightarrow \] \[R=\frac{\rho d{{l}^{2}}}{m}\] or \[R\propto \frac{{{l}^{2}}}{m}\] \[\Rightarrow \] \[{{R}_{1}}:{{R}_{2}}:{{R}_{3}}=\frac{l_{1}^{2}}{{{m}_{1}}}:\frac{l_{2}^{2}}{{{m}_{2}}}:\frac{l_{3}^{2}}{{{m}_{3}}}\] \[=\frac{25}{1}:\frac{9}{3}:\frac{1}{5}=125:15:1\]
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