Q1:

During the measurement of a line by chain or tape in slopes, if the length of the line is 'l' and the height difference between the ends of the line is 'h', then the correction to the measured length is more than by

ANS:B -

Correction due to slope.

Cs = True value - measured value.
= root(L^2 - H^2) - L.

= L x [1- (H^2 / L^2)]^0.5 - L = { L [ 1- 0.5*(H^2 / L^2) + [0.5*(0.5-1)*(H^2 / L^2)^2 / 2] } - L.

= L - L* 0.5*(H^2 / L^2) + L* [0.5*(0.5-1)*(H^2 / L^2)^2 / 2 - L.
= -(H^2)/2L - (H^4)/8*L^3.
So, the correction to the measured length is more than by (H^4)/8*L^3*.