In a vernier calipers, (N+1) divisions of vernier scale coincide with N divisions of main scale. If 1 MSD represents 0.1 mm, the vernier constant (in cm) is :

The vernier constant (also called the least count) is the difference between one division on the main scale and one division on the vernier scale.

Given:

$1\mathrm{MSD}=0.1\mathrm{mm}$

and that $(N+1)\mathrm{VSD}=N\mathrm{MSD}$ (i.e., (N+1) vernier divisions coincide with N main‑scale divisions).

Therefore the total length of N main‑scale divisions is

$N\mathrm{MSD}=N\times 0.1\mathrm{mm}$

Hence one vernier division (VSD) is

$\mathrm{VSD}=\frac{N}{\times }/(N+1)$

The least count (vernier constant) is

$\mathrm{LC}=\mathrm{MSD}-\mathrm{VSD}$

Substituting MSD = 0.1 mm and the expression for VSD:

$\mathrm{LC}=0.1\mathrm{mm}-\frac{N}{\times }/(N+1)$

Factor out 0.1 mm:

$\mathrm{LC}=0.1\mathrm{mm}\times (1-\frac{N}{(})$

Simplify the bracket:

$1-\frac{N}{(}=\frac{1}{}(N+1)$

Thus

$\mathrm{LC}=0.1\mathrm{mm}/(N+1)$

Convert 0.1 mm to centimetres (1 mm = 0.1 cm):

$0.1\mathrm{mm}=0.01\mathrm{cm}$

Therefore the vernier constant in centimetres is

$\mathrm{LC}=\frac{0.01}{\mathrm{cm}}/(N+1)$

which can be written as

$1/100(N+1)$

Hence the correct answer is 1/100(N+1).