For the first order precise levelling, where Distance D is in Km, the permissible error E (in meters) is _______ .
- A± 0.1200 × √D
- B± 0.0250 × √D
- C± 0.0060 × √DCorrect
- D± 0.0006 × √D
Solution
Concept
Levelling accuracy depends on the distance covered. Precise levelling has strict limits on the allowed error to ensure high accuracy.
Formula
E = ± C × √D
Step-by-step solution
1. In surveying, the permissible error (E) in levelling is calculated using the formula E = ± C × √D. 2. Here, E is the error in meters and D is the distance in kilometers (Km). 3. The constant 'C' changes based on the 'order' or quality of the work. 4. For First Order Precise Levelling (the most accurate type), the standard value of C is 0.006. 5. Putting this value in the formula, we get E = ± 0.0060 × √D. Answer: (C) ± 0.0060 × √D
Explanation
First order levelling is used for high-precision work like national benchmarks. The permissible error is kept very low at 6 mm per square root of distance in km. This ensures that errors do not accumulate over long distances.
Why the other options are wrong
A: This value (0.120) is too high and represents very rough or low-grade levelling. B: This value (0.025) is closer to third-order or ordinary levelling limits. D: This value (0.0006) is practically impossible to achieve in field surveying.
Shortcut
Remember the sequence: First order = 6mm (0.006), Second order = 12mm (0.012), Third order = 24mm (0.024).
Common mistake
Students often confuse the units; remember that D must be in Km to get E in meters using these constants.
Correct answer: C) ± 0.0060 × √D