Errors in measurementMedium
Question
In a vernier callipers, $(N + 1)$ 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
A.100 N
B.$10(N + 1)$
C.$\frac{1}{10\text{ }N}$
D.$\frac{1}{100(N + 1)}$
Solution
Sol. [Key Concept: Vernier callipers — least count] V.C $=$ MSD - VSD
given : $(N + 1)VSD = N$ MSD
$$\begin{array}{r} VSD = \left( \frac{N}{N + 1} \right)MSD\#(2) \end{array}$$
From (1) and (2)
$$\begin{matrix} & V.C = (MSD) - \frac{N}{N + 1}(MSD) \\ & \ = MSD\left( 1 - \frac{N}{N + 1} \right) = \frac{MSD}{N + 1} \\ & \ = \frac{0.01}{N + 1} = \frac{1}{100(N + 1)} \end{matrix}$$
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