2024 Units and MeasurementsVernier Calipers and Least Count Easy Question 7 of 53 in Units and Measurements

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:

A $100N$
B $10(N+1)$
C $\frac{1}{10N}$
D $\frac{1}{100(N+1)}$

The answer is D.

Solution

$(N+1)$ VSD $= N$ MSD 1 VSD $= \left(\frac{N}{N+1}\right)$ MSD Vernier constant = 1 MSD $-$ 1 VSD $= 1\ MSD - \left(\frac{N}{N+1}\right) MSD = \left(\frac{1}{N+1}\right) MSD$ $= \frac{1}{N+1} \times 0.1$ mm $= \frac{1}{100(N+1)}$ cm

Concept Vernier constant formula

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