Question #43375

A metre bridge apparatus is mounted inside an elevator. The bridge wire of length $100 \text{ cm}$ is clamped at ends A and B by identical heavy conducting blocks of mass $m$. The contact resistance at each end is inversely proportional to the normal force exerted by the blocks on the wire. The equivalent end corrections at A and B are equal, denoted by $\alpha$ (in cm). When the elevator is stationary, an unknown resistance $X$ in the left gap and a known resistance $R = 60 \ \Omega$ in the right gap produce a null point at a distance $l_1 = 39.0 \text{ cm}$ from end A. When the elevator accelerates upwards at $a = 2.5 \text{ m/s}^2$, the null point shifts to $l_2 = 39.2 \text{ cm}$ from end A. Assuming acceleration due to gravity $g = 10 \text{ m/s}^2$, what is the value of the unknown resistance $X$?