Question

If the pitch of the screw is 1 mm and there are 200 divisions on the circular scale, the least count of the screw gauge will be
(A) 0.01 mm
(B) 0.02 mm
(C) 0.002 mm
(D) 0.005 mm

Answer 1

The least count is the capability of the instrument to measure minimum distance accurately. If we measure something, then the least count gives information about the accuracy of the measurement. We can determine the value of the least count by taking the ratio of the smallest reading value of the main scale and the number of divisions on the auxiliary scale.

Complete step by step answer:
It is given to us that the pitch of the screw is 1 mm, and the circular scale consists of 200 divisions, so use this information in the expression of the least count.
Write the expression of the least count.
$LC = \dfrac{{SR}}{N}$
Here, $SR$ is the smallest reading of the screw gauge, and $N$ is the total number of divisions on the circular scale.
Now we will substitute the given values in the above equation to calculate the least count.
Therefore we get
$\begin{array}{l} LC = \dfrac{{1\;{\rm{mm}}}}{{200}}\\\ LC = 0.005\;{\rm{mm}} \end{array}$
Therefore, if the screw's pitch is 1 mm and 200 divisions are on the circular scale, then the least count of the screw gauge will be 0.005 m, and option (D) is correct.

Note: In these types of questions, the larger number of divisions on the scale will give more accurate division, and if the number of divisions is less, we will get a less accurate measurement. Also, if the options are given in meters, then first convert the value of pitch into the meter and then proceed towards the calculation.