Question

If the pitch of a screw gauge is $0.5mm$ and its least count is $0.01mm$. Find the number of divisions on the head scale.
(A) $50$
(B) $100$
(C) $200$
(D) $500$

Answer 1

Hint We will first start with understanding what the screw gauge is. The micrometer screw gauge is also known as screw gauge is an instrument that is being used in many scientific and engineering experiments such as measuring the diameter of very thin wire, etc. This problem can be solved by using the least count of micrometer screw gauge.
Formula used:
The least count $(L.C)$ of micrometer screw gauge can be given as the ratio of the pitch $(a)$ of the screw gauge to the total number of divisions on the circular scale $(b)$ .
$L.C = \dfrac{a}{b}$

Complete Step by step solution
The micrometer is an instrument that is being used for the measurement of very fine and thin dimensions of the objects and it can provide accuracy up to $ \pm 0.01mm$ . It consists of a U-shaped part in which objects whose dimensions such as diameter in the case of thin wire and thickness and width of other objects are placed in the U-shaped part. It consists of a circular scale and a head scale. The least count of a micrometer provides the smallest and accurate value of the measured quantity.
The least count of a micrometer can be obtained as the ratio of the pitch $(a)$ of the screw gauge to the total number of divisions on the circular scale $(b)$ .
$L.C = \dfrac{a}{b}$ ------------- Equation $(1)$
Here the pitch of the micrometer is given as $a = 0.5mm$and the least count as $L.C = 0.01mm$ . Hence by using these given quantities and substituting them in the equation $(1)$ we will find the total number of divisions on the head scale.
$0.01mm = \dfrac{{0.5mm}}{b}$
$ \Rightarrow b = \dfrac{{0.5mm}}{{0.01mm}}$
Now solving this equation we will get the total number of division on the head scale as
$b = \dfrac{{0.5mm}}{{0.01mm}}$
$\therefore b = 50$
Therefore the total number of divisions on the head scale is $b = 50$ .

Hence option (A) is the correct answer.

Note Some micrometer screw gauge also consists of errors in this measurement that can occur due to improper handling, manufacturing defects, etc. Hence one should always check for errors because errors can cause a slight deviation from the accuracy of the instruments.