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Measuring Instruments and Least Count

The error in the measurement by an instrument is equal to least count of the instrument.
For example, a meter scale has smallest division 1 mm. This represents the least count or the absolute error in the measurement.
Let a length measured by the meter scale = 51.0 cm
This implies that x = 51.0 cm
Absolute error, Δx = 1 mm = 0.1 cm
Relative error, 29710.png

Vernier calipers

Vernier callipers consists of two scales, viz., main scale and vernier scale. Vernier scale moves on the main scale (Figure). The least count of the instrument is the smallest distance between two consecutive divisions and it is equal to 1 MSD – 1 VSD.
In Fig. 1, 1 MSD = 0.1 cm and 1 VSD = 0.09 cm.
Least count = 1 MSD – 1 VSD = 0.01 cm
For the commonly used instruments, least counts are given below:
Least count of Vernier callipers = 1 MSD – 1 VSD

Screw gauge

A screw gauge contains a main scale and a circular scale. The circular scale is divided into a number of divisions. In other words, the complete rotation of circular scale is divided into a number of parts. The least count of a screw gauge is
Least count = 30223.png
If reading on main scale is 5 cm (say) and reading on circular scale is 25 divisions, then the reading is 5 cm + 25 × least count.

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