Section 4: Soil and Water Conservation Engineering
Surveying and Levelling
Subtopic: Types of levelling
Question Statement:
In a reciprocal leveling, the level set up close to point P gave readings of 1.6 m and 0.8 m at stations P and Q respectively. The readings obtained by setting up the level close to point Q were 1.4 m and 0.5 m on stations P and Q respectively. Total error of collimation, curvature and refraction in m is
Options:
(A) 0.05
(B) 0.10
(C) 0.55
(D) 0.85
Official Answer Key:
A
Step-by-Step Solution & Explanation
Reciprocal levelling formula: true difference in level = ½[(P−Q)near P + (P−Q)near Q]; combined error (collimation + curvature + refraction) e = ½[(P−Q)near P − (P−Q)near Q]. (P−Q) near P = 1.6 − 0.8 = 0.8 m. (P−Q) near Q = 1.4 − 0.5 = 0.9 m. e = ½(0.8 − 0.9) = ½(−0.1) = −0.05 m → magnitude 0.05 m, matching option (A). (The true difference in elevation itself is ½(0.8+0.9)=0.85 m, which is the value listed as distractor (D).)
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