In a vernier callipers, (N+1) divisions of vernier scale coincide with N divisions of main scale. If

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1.Units, Dimensions and Measurement

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In a vernier callipers, $(N+1)$ divisions of vernier scale coincide with $N$ divisions of main scale. If $1 \mathrm{MSD}$ represents $0.1 \mathrm{~mm}$, the vernier constant (in $\mathrm{cm}$ ) is:

A

$\frac{1}{100(N+1)}$

B

$100 \mathrm{~N}$

C

$10(N+1)$

D

$\frac{1}{10 \mathrm{~N}}$

(NEET-2024)

Solution

$V \cdot C=M S D-V S D$

$\text { given }:(N+1) V S D=N M S D$ $……..(1)$

$\text { VSD }=\left(\frac{N}{N+1}\right) M S D$

given : $(N+1) \mathrm{VSD}=N \mathrm{MSD}$ $……..(2)$

From ($1$) and ($2$)

$V \cdot C=(M S D)-\frac{N}{N+1}(M S D)$

$=M S D\left(1-\frac{N}{N+1}\right)=\frac{M S D}{N+1}$

$=\frac{0.01}{N+1}=\frac{1}{100(N+1)}$

Standard 11

Physics

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