b
Given, \(R_{1}=35 \Omega, l_{2}=2 l_{1}\)

On increasing the length,

\(m_{1}=m_{2}\)

\(\therefore \rho A_{1} l_{1}=\rho A_{2} l_{2}\)

\(\pi r_{1}^{2} l_{1}=\pi r_{2}^{2} l_{2}\)

\(\frac{r_{1}^{2}}{r_{2}^{2}}=\frac{l_{2}}{l_{1}}\)

\(\frac{r_{1}^{2}}{r_{2}^{2}}=\frac{2 l_{1}}{l_{1}}\)

\(\frac{r_{1}^{2}}{r_{2}^{2}}=2 \ldots(i)\)

\(\frac{R_{1}}{R_{2}}=\frac{\rho \cdot \frac{l_{1}}{\pi r_{1}^{2}}}{\rho \cdot \frac{l_{2}}{\pi r_{2}^{2}}}\)

\(=\frac{l_{1}}{l_{2}} \cdot \frac{r_{2}^{2}}{r_{1}^{2}}=\frac{l_{1}}{2 l_{1}} \cdot \frac{1}{2}\)

\(\frac{R_{1}}{R_{2}}=\frac{1}{4}\)

\(R_{2}=4 R_{1}=4 \times 35=140 \Omega\)