If sensitivity of a bubble tube is 30″ per 2 mm division what would be the error in staff reading on a vertically held staff at a distance of 200 m, when the bubble is out of centre by 2·5 divisions ?
- A0·073 mCorrect
- B0·73 m
- C0·0073 m
- D7·3 m
Solution
Concept
Error due to bubble out of centre
Formula
e = D · θ (radians)
Step-by-step solution
1. Angular error θ = 2.5 × 30″ = 75″ = 75 × 4.848×10⁻⁶ = 3.636×10⁻⁴ rad. 2. Staff reading error = 200 × 3.636×10⁻⁴ = 0.0727 m ≈ 0.073 m.
Explanation
The inclination of the line of sight caused by the displaced bubble multiplied by the distance gives the error in the staff reading.
Why the other options are wrong
0.73, 0.0073 and 7.3 m are powers of ten away from the result.
Shortcut
e = D × θ″ / 206265.
Common mistake
Using 2 mm instead of the number of divisions.
Correct answer: A) 0·073 m