A potentiometer wire 10 m long has a resistance of 40Ω. It is connected in series with a resistance box and a 2V storage cell. If the potential gradient along the wire is 0.1 mV/cm , the resistance in the box is

$760\Omega$

$\text{Potential Gradient is } 0.1 mV/cm = 0.01 V/m$

$\text{Total Potential difference acroee Potentiometer wire is }V = 0.01\times 10V =0.1 V=  40I$

$ I = \frac{1}{400}$

$ Also , 2V = I(R+ 40) $ 

$ R = \frac{2}{I} - 40 = 800 - 40 = 760 \Omega$