Levelling MCQ with answer and solution

Concept

Curvature Correction in Levelling

Formula

Cc = 0.0785 d² (or Cc = d² / 2R)

Step-by-step solution

1. Review the question asking for the nature of curvature correction applied to a staff reading in levelling. 2. Recall that due to the Earth's curvature, staff readings appear higher than true level, making the curvature correction always negative or subtractive (Cc = -0.0785 d²). 3. Compare with the given options and select Option (a) as the correct choice.

Explanation

Because the Earth curves away from the horizontal line of sight, the reading taken on a levelling staff appears higher than it actually is. To get the correct level, the extra height caused by the Earth's curvature must always be subtracted from the observed reading.

Shortcut

To remember curvature vs. refraction corrections, use the phrase "Curvature Cuts, Refraction Raises": - Curvature Correction: Always subtractive/negative (Cc = -0.0785 d²) because curvature makes readings appear higher than true level. - Refraction Correction: Always additive/positive (Cr = +0.0112 d²) because refraction bends light downwards, making readings appear lower.

Common mistake

A common mistake is selecting option C ("Always positive") by confusing curvature correction with refraction correction, which is additive, or by confusing the sign of the error with the sign of the correction. Since Earth's curvature causes the staff reading to appear higher than it actually is (positive error), the correction applied to the staff reading must always be subtractive (negative).