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If the sensitivity of the bubble tube of a level is 30" of arc per division, determine the disn of apoint at which the combined curvature and refraction correction become numerically equalto the error induced by dislevelment of 1 division of the level tube-
  • a)
    2161.13m
  • b)
    2522.24m
  • c)
    2450.62m
  • d)
    2367.26m
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
If the sensitivity of the bubble tube of a level is 30" of arc per...
Solution:

Given data:
Sensitivity of the bubble tube of level (s) = 30 arc/division
Error induced by dislevelment of 1 division of level tube (e) = s/2 = 30/2 = 15 arc

To find: Distance at which combined curvature and refraction correction become numerically equal to the error induced by dislevelment of 1 division of the level tube.

Let d be the distance at which the combined curvature and refraction correction become numerically equal to the error induced by dislevelment of 1 division of the level tube.

Then, the combined curvature and refraction correction (C) is given by:
C = (d/2R) x (d/2) + (d/2R)2 x (d/4)3
where R is the radius of the earth.

Equating C to e, we get:
(d/2R) x (d/2) + (d/2R)2 x (d/4)3 = 15

On solving the above equation, we get: d = 2161.13 m

Therefore, the distance at which the combined curvature and refraction correction become numerically equal to the error induced by dislevelment of 1 division of the level tube is 2161.13 m.

Hence, option A is the correct answer.
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