Q8. In setting up a plane table at station A, the corresponding point on the plan was NOT accurately centred above A. If the displacement of A was 20 cm in a direction at right angles to the ray, how much would be the consequent displacement of a point from its true position on the plan? (Scale: 1 cm = 2 m)
📚 Detailed Explanation: Centering Error & Its Effect on the Plan
This question tests the concept of centering error — the error introduced when the station point on the drawing sheet is not positioned directly above the physical ground station peg. The displacement on the sheet is simply the ground displacement scaled down by the map’s representative fraction (R.F.).
Step-by-Step Solution
• Ground displacement of point A = 20 cm (perpendicular to the ray)
• Map scale: 1 cm on map = 2 m on ground = 200 cm on ground
• Representative Fraction (R.F.) = 1 cm ÷ 200 cm = 1/200
Displacement on plan = Ground displacement × R.F.
Substituting:
Displacement on plan = 20 cm × (1/200)
= 20/200 cm
= 0.1 cm
= 1 mm ✓ (Option C)
Why the Other Options Are Wrong
| Option | Value | Error made |
|---|---|---|
| A | 2 mm | Used R.F. = 1/100 (i.e., scale 1 cm = 1 m) instead of 1 cm = 2 m. This doubles the correct answer. |
| B | 0.4 mm | Used R.F. = 1/500 (i.e., scale 1 cm = 5 m). Incorrect scale applied. |
| D | 0.03 mm | Used R.F. of approximately 1/6000. Far too small; represents an extremely large-scale reduction that does not match the given scale. |
Key Concepts for Students
- Centering error is inversely proportional to scale: The larger the scale (closer to reality), the more significant the centering error on the plan. At a large-scale survey (1 cm = 1 m, R.F. = 1/100), a 20 cm ground error gives 2 mm on the sheet — quite significant for precise work.
- Units must be consistent: Always convert the scale denominator to the same units as the ground displacement before calculating. Here, 2 m = 200 cm, giving R.F. = 1/200. Failing to convert metres to centimetres is the most common arithmetic mistake in this type of problem.
- Plumbing fork prevents centering error: The plumbing fork (U-fork with plumb bob) is the specific instrument designed to prevent centering error. It aligns the sheet point precisely above the ground station. This question illustrates quantitatively why accurate centering matters.