Two resistance \( R_1 = X\Omega \) and \( R_2 = 1\Omega \) are connected to a wire AB of uniform resistivity, as shown in the figure. The radius of the wire varies linearly along its axis from \( 0.2 \, \text{mm} \) at A to \( 1 \, \text{mm} \) at B. A galvanometer (G) connected to the centre of the wire, \( 50 \, \text{cm} \) from each end along its axis, shows zero deflection when A and B are connected to a battery. The value of \( X \) is _____.
![]()
