Two resistances \( R_{1}=X \Omega \) and \( R_{2}=1 \Omega \) are connected to a wire \( A B \) ...

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Two resistances \( R_{1}=X \Omega \) and \( R_{2}=1 \Omega \) are connected to a wire \( A B \) of uniform resistivity, as shown in the figure. The radius of the wire varies linearly along its axis from \( 0.2 \mathrm{~mm} \) at \( A \) to \( 1 \mathrm{~mm} \) at \( B \). A galvanometer \( (G) \) connected to the center of the wire, \( 50 \mathrm{~cm} \) from each end along its axis, shows zero deflection when \( A \) and \( B \) are connected to a battery. The value of \( X \) is
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