Which one is the CORRECT option for the cumulative errors?
1. It decreases with an increase in measurement.
2. It is directly proportional to the length of the line.
3. It may be positive or negative.
4. It is inversely proportional to the length of the line.
📝 Detailed Explanation: Characteristics of Cumulative Errors
Cumulative errors, also known as systematic errors, are errors that consistently occur in the same direction under the same conditions for every measurement. Because of this, their effect builds up or "accumulates" over the course of a survey.
Analysis of the Statements:
1. It decreases with an increase in measurement. (Incorrect)
This is false. The nature of a cumulative error is that it builds upon itself. Therefore, the total error increases as the measurement distance increases.
2. It is directly proportional to the length of the line. (Correct)
This is a defining characteristic. If a chain has a small error in its length, that error is repeated with every chain length measured. The total error is the error per unit length multiplied by the total length, making it directly proportional.
3. It may be positive or negative. (Correct)
The sign of the error depends on the source. For example:
- A chain that is physically too short will consistently produce a positive error (measured distance > true distance).
- A chain that is physically too long will consistently produce a negative error (measured distance < true distance).
4. It is inversely proportional to the length of the line. (Incorrect)
This is the opposite of the correct relationship. As explained in point 2, the error is directly proportional.
Key Takeaway
Cumulative errors are predictable and follow a physical law. Because they are directly proportional to the length of the line (Statement 2) and can be either positive or negative depending on the cause (Statement 3), they can be calculated and corrected for. Common sources include incorrect chain/tape length, temperature effects, and sag.