Correction of length due to reduction to mean sea level is:
Correct Answer: A. directly proportional to measured length
📚 Detailed Explanation: MSL Reduction Correction Is Directly Proportional to Measured Length
Why A (directly proportional to measured length) is correct: When a horizontal distance D is measured at height h above Mean Sea Level, it must be reduced to its equivalent length at MSL using: correction = (h/R) × D. This formula shows the correction is directly proportional to D — double the length, double the correction.
MSL Reduction formula:
correction = (h / R) × D
where: h = height of survey above MSL (m)
R = radius of Earth (≈ 6370 km)
D = measured length at height h
correction = (h / R) × D
where: h = height of survey above MSL (m)
R = radius of Earth (≈ 6370 km)
D = measured length at height h
Proportionality:
correction ∝ D (directly proportional to measured length)
correction ∝ h (also directly proportional to height)
correction ∝ 1/R (inversely proportional to Earth’s radius)
Why Other Options Are Wrong
| Option | Claim | Why Wrong |
|---|---|---|
| A | Directly proportional to measured length | CORRECT — correction = (h/R) × D ∝ D |
| B | Directly proportional to radius of Earth | WRONG — radius R appears in denominator: correction ∝ 1/R |
| C | Inversely proportional to measured length | WRONG — correction increases with D, not decreases |
| D | Inversely proportional to height above MSL | WRONG — correction = h × D / R; it increases with h, not decreases |
- MSL correction = (h/R) × D → directly proportional to measured length (D).
- Also directly proportional to h (elevation above MSL).
- Inversely proportional to R (Earth's radius).