$\int_{0}^{R} d R=k \int_{0}^{1} \frac{d \ell}{\sqrt{\ell}}$

$\mathrm{R}=2 \mathrm{k}$ resistance of wire $\mathrm{AB}$

Again, $\int_{0}^{R / 2} \mathrm{d} \mathrm{R}=\mathrm{k} \int_{0}^{L} \frac{\mathrm{d} \ell}{\sqrt{\ell}} \quad \mathrm{L} \rightarrow$ Length $\mathrm{AP}$

$\frac{\mathrm{R}}{2}=\mathrm{k} 2 \mathrm{L}^{1 / 2} \quad ; \quad \mathrm{k}=\mathrm{k} 2 \mathrm{L}^{1 / 2}$

$\Rightarrow \quad \mathrm{L}=\frac{1}{4}\, \mathrm{m}=0.25 \,\mathrm{m}$