In a vernier calliper, N divisions of vernier scale coincide with (N-1) divisions of main scale (in which division represent 1mm). The least count of the instrument in cm. should be

Options

A. `N`
B. `N-1`
C. `(1)/(10N)`
D. `(1)/((N-1))`

Answer

C

Explanation

As given `N VSD = (N-1) MSD`
`VSD = `Vernier scale division
`MSD =` Main scale division
`1VSD = ((N-1)/(N)) MSD`
`LC =` least count `= 1 MSD - 1 VSD`
`LC = (1-(N-1)/(N)) MSD`
`=(1)/(N) MSD = (0.1)/(N) cm = (1)/(10N)cm`