Chain surveying accuracy — offsets measured with an accuracy of 1 in 40 must meet a plotting tolerance of 0.05 cm at a scale of 1 cm = 20 m. Considering both angular and measurement errors, what is the maximum permissible length of an offset?

Introduction / Context:
Offsets from a chain line carry two principal error sources: (i) error in setting the perpendicular direction and (ii) error in measuring the offset length. For a given drawing scale and allowable displacement on the plan, the maximum offset length must be limited so the combined positional error does not exceed the plotting tolerance.

Given Data / Assumptions:

• Accuracy of offset measurement = 1 in 40 (i.e., length error ≈ L/40).
• Allowable displacement on plan = 0.05 cm.
• Scale = 1 cm : 20 m ⇒ 0.05 cm on plan corresponds to 1 m on ground.
• Angular and linear components are treated as orthogonal and combined by root-sum-square.

Concept / Approach:

Let L be the offset length (ground). With 1 in 40 accuracy, the standard deviation/limit of both the directional (from setting perpendicular) and the linear measurement components can be taken as ≈ L/40 each (conventional exam assumption when only a single accuracy figure is given). The resultant ground-position error ≈ √[(L/40)² + (L/40)²] = (L/40)√2. This must be ≤ 1 m (ground equivalent of 0.05 cm at the stated scale). Solve for L.

Step-by-Step Solution:

Verification / Alternative check:

Even if the two components do not exactly equal each other, using the combined error as above yields a conservative limit close to tabulated values in surveying texts for similar scales and accuracies.

Why Other Options Are Wrong:

14.14 m — overly conservative (half of the allowable limit).
200 m — far exceeds the limit; plan displacement would be much larger than permitted.
None of these — incorrect because 28.28 m satisfies the conditions.

Common Pitfalls:

Forgetting to convert the plotting tolerance to ground units; adding errors arithmetically instead of by root-sum-square when they are independent; ignoring the angular component altogether.

Final Answer:

28.28 m