Question

In a vernier callipers, N divisions of the main scale coincide with N + m divisions of the vernier scale. what is the value of m for which the instrument has minimum least count.

Answer 1

Given:-

N+m (Vernier Scale Divisions) = N ( Main Scale Division)

To Find:-

The value of m for which instrument has minimum least count

Solution:-

We have

1 ( Vernier Scale Division) = $\frac{N}{(N+m)}$  (Main Scale Division)

We know that the value of least count will be i.e

Least Count = 1(Main Scale Division) - 1(Vernier Scale Division).........(1)

putting the value of 1 ( Vernier Scale Division) in above equation (1), then

Least Count (L.C) = [1 - ($\frac{N}{N+m}$)]   (M.S.D)

Small value of denominator find the value of least count i.e If we take m = 1 then the least count will be

L.C = [ 1 -  $\frac{N}{N + 1}$] ( M.S.D) , is the minimum least count for m =1.