Question

Systematic errors lead due to a lack of

• A. \( \text{Gradation of the instrument} \)
• B. \( \text{Significant digits in the measurement} \)
• C. \( \text{Precision in the measurement} \)
• D. \( \text{Accuracy in the measurement} \)

Hint:

Distinguish between Accuracy and Precision: \textbullet \ Accuracy How close a measurement is to the true value. Affected by systematic errors. \textbullet \ Precision How close repeated measurements are to each other. Affected by random errors, and limited by the instrument's resolution/least count. Imagine a dartboard: Accurate shots hit near the bullseye. Precise shots hit close together, regardless of where they land on the board. Systematic errors pull all your shots consistently to one side, affecting accuracy. Random errors cause your shots to scatter, affecting precision.

Answer 1

The Correct Option is A

To solve this problem, let's explore the concept of systematic errors in measurements and the factors that contribute to them.

1. What are Systematic Errors?

Systematic errors are reproducible inaccuracies that occur in the measurement process. Unlike random errors, which fluctuate unpredictably, systematic errors consistently affect measurements in the same way each time. These errors often stem from imperfections or biases in the measurement system or instrument.

2. Causes of Systematic Errors:

Systematic errors can occur due to a variety of factors, including:

• Instrumental errors: These occur when the measuring instrument is not calibrated properly, or has inherent flaws that consistently distort the measurements.
• Environmental errors: External factors such as temperature, pressure, or humidity can cause systematic errors if they are not controlled during measurement.
• Human errors: These include mistakes in reading the instrument, misinterpreting data, or incorrect setup of the measurement process.

3. Explanation of the Options:

- Option 1: "Accuracy in the measurement" – This is incorrect. Accuracy refers to how close a measurement is to the true value. While systematic errors affect accuracy, the presence of systematic errors is not due to a lack of accuracy. Accuracy is the result of minimizing errors.

- Option 2: "Significant digits in the measurement" – This is incorrect. Significant digits refer to the precision with which a measurement is expressed. While significant digits affect the representation of data, they do not directly lead to systematic errors. Systematic errors result from factors such as calibration or environmental influences, not the number of significant digits used.

- Option 3: "Precision in the measurement" – This is incorrect. Precision refers to how consistently measurements can be repeated. Systematic errors are not caused by a lack of precision. In fact, measurements can be highly precise (i.e., consistent) but still inaccurate due to systematic errors.

- Option 4: "Gradation of the instrument" – This is correct. The gradation of the instrument refers to the smallest divisions or markings on the measuring scale. If the gradation is incorrect or poorly defined, it can lead to systematic errors. For example, a miscalibrated instrument with poorly defined gradations may consistently over- or under-read values, leading to systematic errors in all measurements.

4. Why This Matters:

Understanding the sources of systematic errors is essential for improving measurement accuracy. Systematic errors are typically more predictable than random errors and can often be corrected by calibrating instruments, improving measurement procedures, or adjusting for environmental factors. Identifying and minimizing systematic errors ensures that measurements reflect true values as closely as possible.

5. Final Answer:

The correct answer is "Gradation of the instrument."