Question:
Which one of the following statements is TRUE with respect to levelling survey?
Which one of the following statements is TRUE with respect to levelling survey?
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A level surface is an equipotential gravity surface; remember the geoid is the irregular real surface while the ellipsoid is the regular mathematical one.
Updated On: Jul 22, 2026
- A level surface at all points is normal to the direction of the force of gravity.
- Two level surfaces can cross each other.
- Ellipsoid is an irregular surface approximating the physical surface of the Earth.
- Geoid is a regular surface approximating the physical surface of the Earth.
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The Correct Option is A
Solution and Explanation
Step 1: Understanding the Question:
The question asks which basic statement of levelling (the surveying technique used to find elevations) is correct, out of four claims about level surfaces, the ellipsoid and the geoid.
Step 2: Key Formula or Approach:
A level surface is defined as a surface that is, at every point, perpendicular (normal) to the local direction of gravity (the local plumb line). A level line is the trace of a level surface at a given elevation. The geoid is the particular level surface that closely follows mean sea level, and because gravity is not uniform everywhere on Earth (it varies with rock density, topography and latitude), the geoid is an irregular surface. The ellipsoid (spheroid), by contrast, is a mathematically regular, smooth surface used to approximate the geoid for computation.
Step 3: Detailed Explanation:
Statement (A) says a level surface is at all points normal to the direction of the force of gravity. This is exactly the textbook definition of a level surface, so (A) is TRUE.
Statement (B) claims two level surfaces can cross each other. Since every level surface is defined by a constant potential of gravity, and gravity potential increases continuously with elevation, two level surfaces at different elevations cannot intersect, they stay parallel-like and never cross. So (B) is FALSE.
Statement (C) calls the ellipsoid an irregular surface. The ellipsoid is in fact a regular, mathematically defined surface of revolution (an oblate spheroid) used precisely because it is regular and easy to compute with, unlike the geoid. So (C) has the description backwards and is FALSE.
Statement (D) calls the geoid a regular surface. The geoid is the truly irregular, undulating equipotential surface caused by uneven mass distribution in the Earth, so calling it regular is FALSE, it is the geoid that is irregular, and the ellipsoid that is regular.
Step 4: Final Answer:
Only statement (A), that a level surface is at all points normal to the direction of the force of gravity, is TRUE.
The question asks which basic statement of levelling (the surveying technique used to find elevations) is correct, out of four claims about level surfaces, the ellipsoid and the geoid.
Step 2: Key Formula or Approach:
A level surface is defined as a surface that is, at every point, perpendicular (normal) to the local direction of gravity (the local plumb line). A level line is the trace of a level surface at a given elevation. The geoid is the particular level surface that closely follows mean sea level, and because gravity is not uniform everywhere on Earth (it varies with rock density, topography and latitude), the geoid is an irregular surface. The ellipsoid (spheroid), by contrast, is a mathematically regular, smooth surface used to approximate the geoid for computation.
Step 3: Detailed Explanation:
Statement (A) says a level surface is at all points normal to the direction of the force of gravity. This is exactly the textbook definition of a level surface, so (A) is TRUE.
Statement (B) claims two level surfaces can cross each other. Since every level surface is defined by a constant potential of gravity, and gravity potential increases continuously with elevation, two level surfaces at different elevations cannot intersect, they stay parallel-like and never cross. So (B) is FALSE.
Statement (C) calls the ellipsoid an irregular surface. The ellipsoid is in fact a regular, mathematically defined surface of revolution (an oblate spheroid) used precisely because it is regular and easy to compute with, unlike the geoid. So (C) has the description backwards and is FALSE.
Statement (D) calls the geoid a regular surface. The geoid is the truly irregular, undulating equipotential surface caused by uneven mass distribution in the Earth, so calling it regular is FALSE, it is the geoid that is irregular, and the ellipsoid that is regular.
Step 4: Final Answer:
Only statement (A), that a level surface is at all points normal to the direction of the force of gravity, is TRUE.
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