Question

How do you define the least count for Vernier Calipers?

Answer 1

Hint : In this question, we find out the least count of the Vernier caliper by using the scale of the Vernier caliper. It has two main scale divisions or Vernier scale division. Using these scales we find out the least count of the Vernier caliper.

Complete step by step answer: We know that Vernier caliper has two scales. So we find out the difference between these scale divisions to find out the least count of Vernier caliper.
We can also say that the difference of values between one main scale division and one Vernier scale division is equal to the least count of the Vernier scale.
The least count is also known as the Vernier constant of the Vernier calipers.
$Least\text{ }Count\text{ }=\text{ }1\text{ }Main\text{ }Scale\text{ }Division\text{ }\left( MSD \right)\text{ }\text{ }1\text{ }Vernier\text{ }Scale\text{ }Division\text{ }\left( VSD \right).$
Let n division on Vernier calipers be of length equal to that of $\left( n-1 \right)$division on the main scale and the value of 1 main scale division be x.
$n\text{ }division\text{ }on\text{ }Vernier\text{ }=\text{ }\left( n-1 \right)\text{ }x$
$Least\text{ }Count=x-\dfrac{(n-1)x}{n}=\dfrac{x}{n}$
$Least\text{ }Count=\dfrac{\left( Value\text{ }off\text{ }one\text{ }main\text{ }scale\text{ }division \right)}{\left( Total\text{ }no.\text{ }of\text{ }divisions\text{ }on\text{ }Vernier\text{ }calipers \right)}$
Value of one main scale division = 1mm
Total no. of divisions on Vernier = 10
Therefore, L.C = 0.1 mm = 0.01 cm

Note: To understand this question we have to study the Vernier caliper before so we can easily understand the concept of the Vernier caliper we have to know about their scale and the division in the Vernier caliper. The least count is the difference between the one main scale division or one Vernier scale division.