Question

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

Options

• 100 N

• 10(N+ 1)

• \[\frac {1}{10 N}\]

• \[\frac {1}{100(N+1)}\]

Answer 1

In a vernier calliper, (N + 1) divisions of the vernier scale coincide with N divisions of the main scale. If 1 MSD represents 0.1 mm, the vernier constant (in cm) is \[\frac {1}{100(N+1)}\].

Explanation:

According to the question (N + 1)VSD = N MSD

So,1 VSD = (\[\frac {N}{N+1}\])MSD

Now, vernier constant = 1 MSD - 1 VSD

= 1 MSD - (\[\frac {N}{N+1}\])MSD = (\[\frac {N}{N+1}\])MSD

= \[\frac {1}{N+1}\]× 0.1mm = \[\frac {1}{100(N+1)}\]cm