Question

What is the difference between the main scale and Vernier scale?

Answer 1

Hint:In order to solve this question, we are going to first define the Vernier calipers, then, the definitions for the Vernier scale and main scale then, the difference between the main scale and Vernier scale is given based on the number of divisions both the scales have relative to each other.

Formula used: The relation between Vernier scale and main scale division
 \[
  10\,VSD = 9MSD \\
   \Rightarrow 1\,VSD = \dfrac{9}{{10}}MSD \\
 \]
Where, \[VSD\]and \[MSD\]are the Vernier scale division and main scale division respectively.

Complete step-by-step solution:
The Vernier calipers consist of two scales-main scale and Vernier scale. A Vernier scale is used to take an accurate measurement for a reading between two markings on a linear scale which is done by using the mechanical interpolation; thereby increasing resolution and reducing measurement error whereas the scale on the larger, fixed portion of the caliper which gives the most significant digits in the reading is called the main scale.
The difference between the Vernier scale and the main scale is in terms of their divisions for the reading. The Vernier scale consists of \[10\]divisions that are equivalent to the \[9\]divisions on the main scale.
That is:
\[
  10\,VSD = 9MSD \\
   \Rightarrow 1\,VSD = \dfrac{9}{{10}}MSD \\
 \]
Where, \[VSD\]and \[MSD\]are the Vernier scale division and main scale division respectively.
The difference between the one Vernier scale division and one main scale division is called the least count. Mathematically,
\[Least\,count = 1MSD - 1VSD\]
Calculating the least count, we get
\[Least\,count = 1MSD - 0.9MSD = 0.1MSD\]
One main scale division is equal to\[1mm\], thus, one Vernier scale division equals\[0.9mm\].

Note: It is important to note that Vernier caliper is one of the most commonly used measuring instruments. It allows the users to measure the width and distances with much accuracy as compared to the main measuring scale. It is used to measure the distance between the two opposite ends of the surface.