$($c$)$ A $50$ metre long tape has been standardised at $25C$ under a pull of $100N.$ During the field measurements the tape was supported at two points A and B$.$ The elevations of A and B were $110\mathrm{.}385m$ and $110\mathrm{.}120m$ with respect to a local bench mark. Elevation of A above mean sea level is $1163\mathrm{.}853m.$ The temperature and pull during the measurement were $42C$ and $150N$ respectively. Find the corrected length of a tape length reduced to mean sea level.

$[$ Consider radius of earth $=6370KM,$

Coefficient of linear thermal expansion $=11\frac{{10}^{-6}}{}C$

Elasticity modulus of tape $=2{10}^{11}\frac{N}{m^2}]$