Question

In an experiment, a set of readings are obtained as follows: \[ 1.24~\text{mm},\ 1.25~\text{mm},\ 1.23~\text{mm},\ 1.21~\text{mm}. \] The expected least count of the instrument used in recording these readings is _______ mm.

• A. \(0.01\)
• B. \(0.1\)
• C. \(0.05\)
• D. \(0.001\)

Hint:

The least count of an instrument is usually equal to the smallest decimal place shown in the measurements.

Answer 1

The Correct Option is A

To determine the least count of the instrument used in recording the given readings, let's first understand the concept of least count:

The least count of an instrument is the smallest measurement that can be accurately read with that instrument. It essentially determines the precision of the instrument used. In this scenario, the readings recorded are:

• \(1.24 \, \text{mm}\)
• \(1.25 \, \text{mm}\)
• \(1.23 \, \text{mm}\)
• \(1.21 \, \text{mm}\)

When examining these readings, we notice that each measurement is expressed up to two decimal places, indicating the precision of measurement. The precision suggests that measurements can be taken in increments of \(0.01 \, \text{mm}\), which aligns with the smallest difference observable in the recorded values (e.g., difference between 1.23 mm and 1.24 mm).

Comparing the options given:

• \(0.01 \, \text{mm}\): Corresponds to the two decimal precision seen in the data.
• \(0.1 \, \text{mm}\): Implies only one decimal place, which doesn't match the precision of the readings.
• \(0.05 \, \text{mm}\): While it is possible for some instruments, the data shows increments finer than this.
• \(0.001 \, \text{mm}\): This would suggest a third decimal place, which is not evident in the given readings.

Therefore, the correct least count of the instrument used is \(0.01 \, \text{mm}\) as supported by the precision observed in the data.

Hence, the correct answer is \(0.01 \, \text{mm}\).