Question

if nth division of main scale coincides with (n+1)th division of vernier scale find the least count of the vernier .given one main scale division is equal to 'a' units

Answer 1

here is your answer. hope thus will help you

Answer 2

Given data states that the nth division on main scale coincide with $(n+1)^{th}$ division of Vernier scale, least count has to be calculated.

Least count is the difference between the main scale division (MSD) and the Vernier scale division (VSD).

Additional data is that 1 MSD equals "a", therefore,

                                 n MSD = (n+1) VSD

             => ($\frac {n} {n+1}$) MSD = 1 VSD

                                => 1 MSD = a

             => 1 VSD = ($\frac {n} {n+1}\times a$)

            => Least Count = a – $(\frac {na} {n+1}) = (\frac {a} {n+1})$