Question

The diagram is a paper of micrometer screw gauge. What is the reading shown? Assume the pitch is $ 0.5mm $

A. $ 4.01mm $
B. $ 4.51mm $
C. $ 5.00mm $
D. None of these

Answer 1

Hint :In this question, we need to determine the reading of the micrometer screw gauge such that the pitch is 0.5 millimeters. First, we need to calculate the least count of the screw gauge. For this, we will recall the terms involved while measurements using a micrometer screw gauge.

Complete Step By Step Answer:
A micrometer screw gauge is used for measuring very small distances. It is used to measure small thickness of papers, wires and other minute items. A micrometer screw gauge has two scales – the linear scale and the circular scale.
The pitch of the screw gauge is calculated by dividing the distance moved by the linear scale in one turn of the circular scale by the number of divisions of the circular scale. In this question, the pitch is directly given to use.
Given,
The pitch of the micrometer screw gauge is $ 0.5mm $
Thus the least count of the screw gauge is given by
 $
  L.C = \dfrac{{pitch}}{\text{no.of circular divisions}} \\
   = \dfrac{{0.5mm}}{{50}} \\
   = 0.01mm \\
  $
Now we see that the linear scale reading is $ 4.5mm $ and the circular scale has turned $ 1 $ divisions
Hence the final reading can be calculated by the formula
 $ M = L.S.D + C.S.D \times L.C $
We put all the values here and then get the reading
 $
  M = 4.5mm + 1 \times 0.01mm \\
   = 4.51mm \\
  $
Hence option (B) is correct.

Note :
Vernier calipers may also be used to measure small distances. However a micrometer screw gauge can measure even smaller distances compared to the Vernier Calipers. Students should also know how to calculate the pitch of the micrometer screw gauge. Also the students should make sure there is no zero error. If any zero error is present it should be subtracted from the final reading.