Measurements

1. Experiments based on vernier CALIPERS & screw gauge

A meter scale can measure accurately up to one–tenth part of one cm. Its least measurement 0.1 cm, is called least count of scale. There is limitation of meter scale that the meter scale cannot measure the value less than 0.1 cm. For greater accuracy measurement we have devices such as,

(i) Vernier Callipers

(ii) Screw Gauge

(i) Vernier Callipers: A vernier callipers provides with an auxiliary (or vernier) scale in addition to the main scale. The vernier scale can slide along the main scale. The vernier scale is so graduated (or marked) that the length of total number of divisions on it is smaller by length of one division on main scale.

The least count of vernier scale is calculated by using the following formula

Least count of vernier scale (or vernier constant)=$\frac{\text{value of 1 main scale division}}{\text{Total number of division on vernier scale n}}$

or

Least count (vernier constant) = 1 M.S.D.(Main scale division) – 1 V.S.D.(vernier scale division).

Example-1 If N division of vernier coincides with (N – 1) division of main scale. Given one main scale division is equal to 'a unit', find the least count of the vernier.

Solution: Vernier constant = 1MSD – 1VSD = $\left(1-\frac{\text{N}-1}{\text{N}}\right)$MSD = $\frac{\text{a }}{\text{N}}$,

Generally, the value of 1 main scale division on vernier callipers is 0.1 cm and there are 10 divisions on the vernier scale, i.e., x = 0.1 cm and n = 10.

$\therefore$ Least count of vernier callipers =$\frac{\text{0}\text{.1 cm}}{\text{10}}$ = 0.01 cm.

Zero error of vernier callipers: If the zero marking of main scale and vernier callipers does not coincide, necessary correction has to be made for this error which is known as zero error of the instrument. If the zero error of the vernier scale is to the right of the zero of the main scale the zero error is said to be positive & the correction will be negative otherwise vice versa.

(ii) Screw gauge:

Least count = $\frac{\text{Pitch }}{\text{Total number of division n on the circular scale}}$

Zero error of screw gauge: In a perfect instrument the zeros of the main scale and circular scale coincides with each other, In this condition screw gauge has zero-error, otherwise the instrument is said to have zero-error which is equal to the cap reading with the gap closed. This error is positive when zero line or reference line of the cap lies above the line of graduation and corresponding corrections will be just opposite otherwise vice-versa.

Example-2 What will be the measurement of following screw gauge position?

Solution: Reading = Main scale reading + Number of circular scale division(or screw gauge reading)xleast count

3mm + 45x 0.01mm = 3.45 mm