# Vernier Callipers | Least Count

Vernier calliper is a precision instrument used to measure internal and external distances accurately upto (1/10)th of a millimetre. The vernier calliper is as shown in the figure 1.

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Vernier Constant (VC): It is the difference between values of one main scale division and one vernier scale division of vernier callipers. Let n vernier scale divisions (VSD) coincide with (n – 1) main scale divisions (MSD).

n VSD = (n – 1) MSD

Vernier constant, VC = 1 MSD – 1 VSD

Vernier constant is also known as vernier calliper least count.

Place the body between the jaws and the zero of vernier scale lies ahead of Nth division of main scale. Then

Main scale reading (MSR) = N

If nth division of vernier scale coincides with any division of main scale, then

Vernier scale reading (VSR) = n × (VC)
Total reading = MSR + VSR = N + n × (VC)

## Zero error

When the jaws A and B touch each other and if the zero of the vernier scale does not coincide with the zero of the main scale, then the instrument has error called zero error. Zero error is always algebraically subtracted from the observed reading.

### Positive zero error

Zero error is said to be positive if the zero of the vernier scale lies on the right of the zero of the main scale as shown
in figure 2. Here, zero error = 0.00 cm + 5 × VC

### Negative zero error

Zero error is said to be negative if the zero of the vernier scale lies on the left of the main scale as shown in figure 3. Here, zero error = 0.00 cm – (10 – 5) × VC

## Excercise

Q. In a vernier callipers, N divisions of vernier scale coincide with (N–1) divisions of main scale in which one division represents 1 mm. The least count of the instrument in cm should be

a). N
b). N – 1
c). 1/10N
d). 1/(N-1)

Answer.       N V.S.D. = (N – 1) M.S.D.

Least count = VC = 1 M.S.D. – 1 V.S.D.

so, option (c) is correct.

Q. A vernier calliper with 20 divisions on the sliding scale, coinciding with 19 main scale divisions where smallest division on the main scale is 1 mm. Calculate least count of the vernier calliper.

Answer. Least count of vernier callipers = 1 M.S.D. – 1 V.S.D.

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