Question

In a vernier calliper $N$ divisions of vernier scale coincides with $\left(\right. N - 1 \left.\right)$ divisions of the main scale (in which length of one division is $1 \, mm$ ). The least count of the instrument should be (in $cm$ ):

• A. $\frac{1}{N - 1}$
• B. $\frac{1}{10 N}$
• C. $N - 1$
• D. $N$

Answer 1

Answer: (B)

Least count $1 \, M S D - 1 V S D$
$= 1 M S D - \left(\right. \frac{N - 1}{N} \left.\right) M S D$
$\because N V S D = \left(\right. N - 1 \left.\right) M S D$
$\therefore 1 V S D = \left(\right. \frac{N - 1}{N} \left.\right) M S D$
$\therefore $ Least count $= \frac{1}{N} M S D = \left(\right. \frac{1}{N} \left.\right) \times \left(\right. \frac{1}{10} \left.\right) c m = \left(\right. \frac{1}{10 \, N} \left.\right)$