Question

Name the instrument which has the least count of \[0.01\,mm\].
A. Ruler
B. Vernier caliper
C. Screw gauge
D. None of the above

Answer 1

Hint: We find out the least count of the main scale of given measuring instruments. The least count of the instrument is the ratio of least count of main scale and the number of divisions on the secondary movable scale.

Complete step by step answer:
Least Count is the smallest value that can be measured precisely by the measuring device. The quantity measured by a measurement device with known LC has high accuracy and repeatability.
Least Count of a measuring device is calculated by taking the ratio of main scale (fix scale) least count to the number of divisions on the secondary scale (movable scale).
We have to determine the least count of every given option.
$Ruler$
The smallest reading on the ruler that we can measure is 1 mm. Therefore, the least count of rulers is 1 mm.
Therefore, the option (A) is incorrect.
$Vernier calliper$
We measure the LC of main scale of Vernier Caliper as follows,
The smallest reading on the main scale of Vernier Caliper is \[1\,{\text{cm}}\]. The number of divisions on the Main scale is 10.
The LC of the main scale of Vernier Caliper is the ratio of smallest reading on the main scale to the number of divisions on the main scale.
\[
{\text{LC of main scale}} = \dfrac{{1\,{\text{cm}}}}{{10}} \\
= 0.1\,{\text{cm}} \\
\]
The total number of divisions of the secondary scale of Vernier Caliper is 50.
Determine the LC count of Vernier Caliper by taking the ratio of main scale least count to the number of divisions on the secondary scale as follows,
\[
{\text{LC}} = \dfrac{{0.1\,{\text{cm}}}}{{50}} \\
= 0.002\,{\text{cm}} \\
\]
Therefore, the option (B) is incorrect.
Screw gauge
The least count of the main scale of screw gauge is 1 mm and the number of divisions on the secondary scale of the screw gauge are 100.
Therefore, the least count of screw gauge is,
\[LC = \dfrac{{1\,mm}}{{100}}\]
\[ \Rightarrow LC = 0.01\,mm\]

So, the correct answer is “Option C”.

Note:
Least Count is not the smallest reading on the main scale divided by the number of divisions on the main scale. Least count on the main scale of both vernier caliper and screw gauge is 0.1 mm but the number of divisions on the secondary scale of both are different.