If `n^(th)` division of main scale coincides with `(n + 1)^(th)` divisions of vernier scale. Given one main scale division is equal to 'a' units. Find the least count of the vernier.

Answer

A

Explanation

`(n + 1) division of vernier scale = n divisions of main scale`.
:. One vernier division `= (n)/(n+ 1)` main scale division
Least count = `1M.S.D - 1VS.D = (1 -(n)/(n + 1)) MSD`
`=(1)/(n + 1)M.S.D. = (a)/(n + 1)units` `[because 1MSD = a units]`