A) r
B) \[\frac{r}{\sqrt{2}}\]
C) \[\sqrt{5}\,\,r\]
D) 2r
Correct Answer: C
Solution :
Resistance, \[R=\frac{\rho l}{A}\] For wire P, \[20=\frac{\rho l}{\pi {{r}^{2}}}\] ?..(i) Similarly, for wire Q, \[8=\frac{\rho (2l)}{\pi {{(r)}^{2}}}\] ?.. (ii) Dividing Eq. (i) by Eq. (ii), we have \[\frac{20}{8}=\frac{\rho l}{\pi {{r}^{2}}}\times \frac{\pi {{(r)}^{2}}}{\rho (2l)}\] \[\Rightarrow \] \[5={{\left( \frac{r}{r} \right)}^{2}}\] \[\Rightarrow \] \[r=\sqrt{5}\,r\]
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