Question 33: Units , Dimensions and Error Analysis

Question

In an experiment, a set of reading are obtained as follows - 1.24 mm, 1.25 mm, 1.23 mm, 1.21 mm. The expected least count of the instrument used in recording these readings is _______ mm.

Accepted Answer

The least count of an instrument is the smallest measurement that can be taken accurately with that instrument. The least count is shown by the position of the last significant digit (the smallest decimal place) to which all readings are recorded.
The obtained readings are :
1. Reading 1 : 1.24 mm
2. Reading 2 : 1.25 mm
3. Reading 3 : 1.23 mm
4. Reading 4 : 1.21 mm
All the readings are recorded up to two decimal places.
The difference between consecutive possible readings
$$ \begin{gathered} 1.25 \mathrm{~mm}-1.24 \mathrm{~mm}=0.01 \mathrm{~mm} \ 1.24 \mathrm{~mm}-1.23 \mathrm{~mm}=0.01 \mathrm{~m} \end{gathered} $$
If the least count were 0.1 mm (the smallest decimal place is 1 ), the readings would look like 1.2 mm or 1.3 mm .
If the least count were 0.001 mm (the smallest decimal place is 3 ), the readings would look like 1.240 mm .
If the least count were 0.05 mm , the readings would only end in .00 or .05 (e.g., $1.20,1.25$ ). Since we have 1.24 and 1.23, this is not possible.
Therefore, the least count of the instrument is 0.01 mm . Hence, the correct option is (A).

Answer

0.01

Answer

0.05

Answer

0.001

Answer

0.1

Units , Dimensions and Error Analysis

In an experiment, a set of reading are obtained as follows - 1.24 mm, 1.25 mm, 1.23 mm, 1.21 mm. The expected least count of the instrument used in recording these readings is _______ mm.

Choose the correct answer: