Question

In four complete rotations, the distance moved by the screw on the linear scale is $2mm$.Its circular scale contains 50 divisions. Find the least count of the screw gauge.
A) $0.05mm$
B) \[0.01mm\]
C) \[0.1mm\]
D) \[0.02mm\]

Answer 1

Hint-For every length measuring instrument, there are divisions. And the minimum measurement taken using the particular instrument is called the least count of that instrument. The least count is specific for every instrument. It is based on the number of divisions that instrument has. The least count is used for the finding the possible error can be made by one.

Complete step by answer:
(i) The screw gauge is used for measuring the radius of the cylindrical objects like wire etc.
(ii) The screw gauge has 50 divisions. If four rotations mean,\[50 \times 4 = 200\]divisions. The distance measured is $2mm$ for 200 divisions. We know that the least count is the minimum measurement measured by any instrument. Therefore,
\[{\text{Least count = 1 division}}\]
 \[{\text{1division = }}\dfrac{{\text{2}}}{{{\text{200}}}}{\text{mm}}\]
Therefore least count =\[0.01mm\].

Hence the correct option is B.

Additional information:
(i) The minimum measurement that we can measure using the particular instrument is called the least count. For example, we use the \[15cm\]. In that scale the minimum value we can measure is \[1mm\]. Hence the least count value is \[1mm\].
(ii)The least count is related to the precision and accuracy of the instrument. So it is directly proportional to the error of the instrument.
(iii)Finding the least count is very much helpful for the instruments like screw gauge, vernier caliper etc.

Note: The minimum division is any instrument is the least count of that instrument. The error of any instrument can be found by using the least count of the instrument. The error percentage is equal to the ratio of difference between the actual value and the real value and least count.