$\left. \begin{matrix} {{L}_{1}}={{\mu }_{{}^\circ }}\frac{{{A}_{1}}N_{1}^{2}}{{{\ell }_{1}}} \\ {{L}_{2}}={{\mu }_{{}^\circ }}\frac{{{A}_{2}}N_{2}^{2}}{{{\ell }_{2}}} \\ \end{matrix} \right\}\Rightarrow \frac{{{L}_{2}}}{{{L}_{1}}}=\frac{{{\mu }_{{}^\circ }}\frac{{{A}_{2}}N_{2}^{2}}{{{\ell }_{2}}}}{{{\mu }_{{}^\circ }}\frac{{{A}_{1}}N_{1}^{2}}{{{\ell }_{1}}}}\xrightarrow[{{N}_{2}}=2{{N}_{1}}=200]{{{\ell }_{1}}={{\ell }_{2}}}\frac{{{L}_{2}}}{{{L}_{1}}}=\frac{0/005\times {{(200)}^{2}}}{0/01\times {{(100)}^{2}}}\Rightarrow \frac{{{L}_{2}}}{{{L}_{1}}}=0/5\times 4=2$