Civil Engineering - UPSC Civil Service Exam Questions - Discussion
Discussion Forum : UPSC Civil Service Exam Questions - Section 14 (Q.No. 41)
41.
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
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Discussion:
3 comments Page 1 of 1.
Krish Pandit said:
5 years ago
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*.
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*.
(2)
Sangeetha said:
5 years ago
Cslope = Actual length - Measured length.
= sqrt(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.
Hence, correction to the measured length is more than by (H^4)/8*L^3.
= sqrt(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.
Hence, correction to the measured length is more than by (H^4)/8*L^3.
(2)
Drone said:
8 years ago
How? someone explain.
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