First slide

Measurement

Question

$N$ divisions on the main scale of a vernier callipers coincide with $N + 1$ divisions on the vernier scale. If each division on the main scale is of a units determine the least count of the instrument.

Moderate

A

$\frac{2 a}{N + 1}$
B

$\frac{a}{N + 1}$
C

$\frac{a}{N + 2}$
D

$\frac{a}{N + 4}$

Solution

(N+1) divisions on the vernier scale = N divisions on main scale
1 division on vernier scale = $\frac{N}{N + 1}$ divisions on main scale
Each division on the main scale is of a units.
1 division on vemier scale = $(\frac{N}{N + 1}) a u n i t s = a^{'}$ (say)
Least count =1 main scale division -1 vernier scale division
Least count = $a - a^{'} = a - (\frac{N}{N + 1}) a = \frac{a}{N + 1}$

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