In a meter bridge, the wire of length $1 m$ has a non-uniform cross-section such that, the variation $\frac { d R } { d l }$ of its resistance $R$ with length $l$ is $\frac { d R } { d l } \propto \frac { 1 } { \sqrt { l } }$. 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 $AP$?\\
(1) 0.2 m\\
(2) 0.35 m\\
(3) 0.3 m\\
(4) $0.25 m$