A) \[{{\operatorname{nR}}_{o}}\]
B) \[{{\operatorname{n}}^{2}}{{R}_{o}}\]
C) \[2{{\operatorname{nR}}_{o}}\]
D) \[2{{n}^{2}}{{R}_{o}}\]
Correct Answer: B
Solution :
\[{{\ell }_{1}}={{\ell }_{\operatorname{o}}}\,\,\,\,\,\,\,\,\,\,\,{{\ell }_{2}}=\operatorname{n}{{\ell }_{o}}\] If wire is elongated but its volume remains constant \[\operatorname{V}{{~}_{initial}}={{V}_{final}}\] \[\pi {{\operatorname{r}}^{2}}_{\operatorname{o}}{{\ell }_{\operatorname{o}}}={{\pi }^{2}}_{2}n{{\ell }_{\operatorname{o}}}\] \[{{r}^{2}}_{2}=\frac{{{\operatorname{r}}^{2}}_{\operatorname{o}}}{n}\] \[{{\operatorname{R}}_{o}}=\rho \frac{{{\ell }_{\operatorname{o}}}}{\pi {{\operatorname{r}}^{2}}_{o}}\] ?(1) \[\operatorname{R}''=\rho \frac{\operatorname{n}{{\ell }_{\operatorname{o}}}}{\pi {{\operatorname{r}}^{2}}_{2}}\] By (1) & (2) \[\operatorname{R}''={{n}^{2}}{{R}_{o}}\]
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