Question

Systematic errors lead due to a lack of

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

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

Errors in measurement can generally be categorized into random errors and systematic errors. \textbullet \ Systematic errors are errors that consistently shift the measurements in one direction from the true value. They are often due to a fault in the instrument, method, or observer that is consistently applied. Examples include: \quad \textbullet \ Instrument calibration errors (e.g., a scale that consistently reads 1 kg too high). \quad \textbullet \ Zero error (e.g., a voltmeter that doesn't read zero when nothing is connected). \quad \textbullet \ Environmental factors (e.g., temperature consistently affecting a sensor's reading). \quad \textbullet \ Consistent observer bias. Systematic errors directly affect the accuracy of a measurement. Accuracy refers to how close a measurement is to the true or accepted value. If systematic errors are present, the measurements will consistently deviate from the true value, leading to low accuracy, even if the measurements are precise (i.e., close to each other). Let's look at the other options: (B) \( \text{Significant digits in the measurement} \): Significant digits relate to the precision of a measurement and how it's reported, not directly to the cause of systematic errors. (C) \( \text{Precision in the measurement} \): Precision refers to the closeness of two or more measurements to each other. Systematic errors do not necessarily affect precision; a systematically erroneous instrument can still produce precise (but inaccurate) readings. For example, a broken ruler might consistently measure objects as 1 cm longer (systematic error), but repeated measurements of the same object might still yield results very close to each other (high precision). (D) \( \text{Gradation of the instrument} \): Gradation (or least count) refers to the smallest division on an instrument's scale. While it relates to the instrument's precision, it's not the primary cause of systematic errors. A poorly calibrated instrument, regardless of its gradation, will suffer from systematic errors. Therefore, systematic errors fundamentally lead to a lack of accuracy in the measurement.