Question

The pitch of a screw gauge is 0.5mm and there are 100 divisions on its circular scale. The instrument reads +2 divisions when nothing is put in between its jaws. In measuring the diameter of a wire, there are 8 divisions on the main scale and 83 divisions coincide with the reference line. Then the diameter of the wire is:

Answer 1

Hint: In this question, we will first know about the screw gauge. Further, by using the formula of least count, we find the least count of the screw gauge and find the thickness of the given wire. Also, we will study in detail about the screw gauge structure, for better understanding.

Formula used:
$L.C = \dfrac{{0.5}}{{100}}mm$

Complete answer:
As we know that the screw gauge is defined as an instrument that is used for measuring exactly the diameter of a thin wire or the width of a sheet of metal with very less error.

Here, least count of the screw gauge is given as:
$L.C = \dfrac{{0.5}}{{100}}mm$
$L.C = 5\mu m = 0.005mm$

Let us find the diameter of the wire:
$thickness = 81 \times 5 = 405$

So, the diameter of the wire is given as (mm) $\ 4.05mm$. Therefore, we get the required answer.

Additional information:
A screw gauge comprises a U-shaped mount. This is fixed with a screwed pin which is further fixed to a thimble. Also, side by side to the axis of the thimble, a scale passed in mm is inscribed. With this U shaped metallic mount, a screw gauge measures even the tiniest length and thinnest thickness with exact accuracy.
The main part of the device checks the exactness and also stops the object from getting ruined. The key scale reading is taken considering also the 0.5 mm divisions that are given below the key scale.
As there are some very important uses of screw gauge, there is also a certain disadvantage of a screw gauge. The disadvantage of the micrometer screw gauge was that its measuring capability was very much limited and so the other instruments had this advantage. If we take an example of the use of screw gauge in daily practice, one of its limitations that were implemented in the lab was that the micrometer screw gauge couldn't measure the internal diameter of the hollow cylinder.

Note:
Screw gauge is a very essential measuring tool, as it has very high accuracy of measuring thinnest and the tiniest length. We should take care of the instrumental error, so before working with the screw gauge, do not forget to check the instrumental error and the least count of the screw gauge.