Question

Least Count of screw gauge is defined as:
$\begin{align}
  & \text{A}\text{. }\dfrac{\text{distance moved by the thimble on main scale}}{\text{number of rotations of thimble}} \\
 & \text{B}\text{. }\dfrac{\text{pitch of the screw}}{\text{number of circular scale divisions on head scale}} \\
 & \text{C}\text{. }\dfrac{\text{number of rotations of thimble}}{\text{number of circular scale divisions}} \\
 & \text{D}\text{. None of the above} \\
\end{align}$

Answer 1

Hint: Least count of a screw gauge is the minimum length that we can measure using a screw gauge. We can measure the least count of the screw gauge by measuring the pitch of the screw gauge and the number of divisions on the circular scale.

Complete step by step answer:

First let’s look at the structure of the screw gauge to understand the process of measuring least count.

As you can see there are two scales on the screw gauge -
(a) Linear Scale
(b) Circular scale

Linear scale is the main scale which is determined to measure the rough length of the object. Circular scale is used to measure the fine values.

The main scale is marked on a hollow cylinder which can move along with the screw.

The circular scale is also movable and marked with several divisions. The number of divisions varies from one screw gauge to another. However, in general the number of divisions is either 100 or 50.

The circular scale is specially designed such that the cylinder moves by 1mm after one complete rotation of the circular scale. So, this gives us an estimate of the least count of the screw gauge.
As the least count of the screw gauge is useful to determine the least amount of length that you can measure, we can divide the pitch of the screw gauge by the total number of divisions to know the least count.

The special design of the circular scale enables us to easily measure the pitch of the screw gauge.

Hence, the least count of screw gauge is given by,
$\dfrac{\text{pitch of the screw}}{\text{number of circular scale divisions on head scale}}$

So, the correct option is (B).

Note:
Screw Gauge is more accurate than the Vernier Caliper. However, both are used for different scenarios. For example, Screw Gauge is mainly used to measure the diameter of thin wires, the thickness of sheet, glass, foil, etc. The most common type of Screw Gauge is called micrometer, which can measure upto 0.001cm or 1µm.