Question

Which one of the following statements is TRUE with respect to levelling survey?

• A. A level surface at all points is normal to the direction of the force of gravity.
• B. Two level surfaces can cross each other.
• C. Ellipsoid is an irregular surface approximating the physical surface of the Earth.
• D. Geoid is a regular surface approximating the physical surface of the Earth.

Hint:

A level surface is an equipotential gravity surface; remember the geoid is the irregular real surface while the ellipsoid is the regular mathematical one.

Answer 1

The Correct Option is A

Levelling survey rests on a small set of definitions: level surface, level line, the geoid and the ellipsoid. Let's test each option against these definitions.

1. A level surface at all points is normal to the direction of the force of gravity: This is the standard definition used in every surveying textbook, a level surface is an equipotential surface of gravity, and at every point on it the direction of gravity (the plumb line) is perpendicular to the surface. This statement is TRUE.
2. Two level surfaces can cross each other: Level surfaces correspond to different, increasing values of gravity potential as elevation increases, so surfaces at two different elevations cannot meet or cross, they remain distinct and roughly parallel. This statement is FALSE.
3. Ellipsoid is an irregular surface approximating the physical surface of the Earth: The ellipsoid (or spheroid) is chosen precisely because it is a smooth, regular, mathematically defined shape, an oblate ellipse rotated about the polar axis, so this description is backwards. This statement is FALSE.
4. Geoid is a regular surface approximating the physical surface of the Earth: The geoid is the irregular, wavy equipotential surface that follows mean sea level and bends with variations in the Earth's mass distribution, so calling it regular is incorrect. This statement is FALSE.

Between the ellipsoid and the geoid, it helps to remember that the geoid is the real, physically defined but irregular surface, while the ellipsoid is the artificial, regular surface used to replace it for calculation. Options (C) and (D) simply swap these two properties.

Let's summarize:

• Level surface: normal to gravity at every point, this is TRUE and matches option (A).
• Level surfaces at different elevations never cross.
• Geoid = irregular, real equipotential surface. Ellipsoid = regular, mathematical surface.

So the correct TRUE statement is option (A).