In a meter bridge, the wire of length $1\, m$ has a nonuniform cross-section such that, the variation $\frac{{dR}}{{d\ell }}$ of its resistance $R$ with length $\ell $ is $\frac{{dR}}{{d\ell }} \propto \frac{1}{{\sqrt \ell }}$ 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 $AP$ ? ................ $m$
JEE MAIN 2019, Diffcult
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