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What is the difference between the Vernier constant and least count of a Vernier caliper?
Vernier Constant: it is the ratio of smallest division of main scale to the number of divisions of vernier scale.
Least Count: the smallest possible measure that any instrument can do accurately is known as least count.
Vernier constant is the difference between the smallest division of main scale and that of vernier scale. When we multiply the vernier constant with the count of one division of main scale we get least count of the vernier caliper.
The quantity represents the difference between the size of the smallest division on the main scale and the size of one Vernier divisions.This
quantity $(S-V)$ is called the Vernier Constant.
I think vernier constant is only the least count of vernier callipers while least count can be of any instrument