N divisions on the main scale of a vernier calipers coincide with (N +1) division of the vernier scale. If each division of main scale is a units, then the least count of the calipers is :

Options

A. `(a)/(N)`
B. a
C. `(a)/(N+1)`
D. `(Na)/(N+1)`

Answer

C

Explanation

Given , N divisions of main scale,
`N_("MSD")= (N+1)` divisions of vernier scale `(N+1)_("VSD") `
`rArr` value of of 1 VSD ` = (N)/(N+1)` MSD
Least count of vernier calipers , LC = 1 MSD - 1 VSD
`1 MSD-(N)/(N+1) MSD`
`= ((N +1 - N)/(N+1))MSD = ((1)/(N+1))MSD`
or `LC = (a)/(N+1)" "` (Given, 1 MSD = a)