In a meter bridge, the wire of length 1 m has a nonuniform cross-section such that, the variation $\frac{\mathrm{dR}}{\mathrm{dl}}$ of its resistance R with length I is $\frac{\mathrm{dR}}{\mathrm{dl}} \propto \frac{1}{\sqrt{\mathrm{l}}}$. Two equal resistances are connected as shown in the figure. The galvanometer has zero deflection when the jockey is at point P . What is the length AP ?