The pitch of a screw gauge is $0.5mm$ and the head scale is divided in $100$ parts. What is the least count of the screw gauge?
A) $0.5mm$ or $0.05cm$
B) $0.05mm$ or $0.005cm$
C) $0.005mm$ or $0.0005cm$
D) $0.0005mm$ or $0.00005cm$

Hint: To solve this question we should know what the least count of any instrument is. It is the smallest measurement that can be made directly from the instrument. We simply have to find the length for each head scale division where the total length of the head scale is $0.5mm$.

Formulae used:
$L.C = \dfrac{{pitch}}{{divisio{n_{c.s}}}}$
Here $L.C$ is the least count of the screw gauge, $pitch$ is the distance moved by the circular scale in one rotation, and $divisio{n_{c.s}}$ is the number of divisions on the circular head scale.

Complete step by step answer:
To start with, let’s see what the least count of a screw gauge means.
Least count can be defined as the smallest, most accurate, direct measurement we can take from any screw gauge. The less is the least count the more precise is the measurement. The least count can be calculated using the formulae,
$L.C = \dfrac{{pitch}}{{divisio{n_{c.s}}}}$
Here $L.C$ is the least count of the screw gauge, $pitch$ is the distance moved by the circular scale in one rotation, and $divisio{n_{c.s}}$ is the number of divisions on the circular head scale.
In the question, the pitch is given to be $0.5mm$ and the number of divisions on the circular head scale is $100$. So the least count of the given screw gauge is,
$ \Rightarrow L.C = \dfrac{{0.5mm}}{{100}} = 0.005mm = 0.0005cm$

So option (C) is the correct answer.

Additional Information:
A screw gauge is an instrument that is used to measure the diameter of thin sheets, wires, or plates. Its pitch can be defined as the distance moved by the circular scale, in one rotation, on the main scale.

Note: While solving questions related to least count, be cautious of the formulae. Always use the correct formulae. Also, the unit is very important. The use of wrong units gives an incorrect answer. So the units must be used properly.