First slide

Measurement

Question

In a Vernier calipers, $N$ divisions of the main scale coincide $N + m$ divisions of the Vernier scale. What is the value of m for which the instrument has minimum least count?

Moderate

A

2
B

1
C

0.1
D

10

Solution

$(N + m) VSD = (N) MSD$
$1 V S D = (\frac{N}{N + m}) MSD$
$L C = 1 MSD - 1 VSD = 1 MSD - (\frac{N}{N + m}) MSD$
$= \frac{m}{N + m} MSD = (\frac{1}{1 + N / m}) MSD$
Now, least count will be minimum for m=1.

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