Question

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 ______.

Options

• `1/(10 N)`

• `1/(100 (N + 1))`

• `1/(100 N)`

• `1/(10 (N + 1))`

Answer 1

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 `bbunderline(1/(100 (N + 1)))`.

Explanation:

Let us assume MSD is a Main Scale Division.

VSD stand for vernier Scale Division.

According to the question:

(N + 1)VSD = N MSD

So, VSD = `(N/(N + 1)) MSD`

Now vernier constant (VC) = MSD − VSD

= `MSD - (N/(N + 1)) MSD`

= `(1/(N + 1)) MSD`

= `1/(N + 1) xx 0.1` mm

= `1/(100(N + 1)` cm