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Experiment-1 Concept of least count


Least Count

For the measurement of a physical quantity say length, angle, temperature, pressure etc, a scale is used.It is a graduated scale and calibrated. A quantity can be measured to a value precisely to a value given by the smallest graduation (which is the least count of the scale) Using a vernier scale, the least count is considerably lowered.

Let us consider two scales whose minimum graduations are represented as


It is seen that the physical quantity can be measured precisely to accuracy A with first scale, to accuracy B with second scale. However when both the scales are present, the quantity can be measured to an accuracy C=(A-B).

In other words, A is the least count of first scale, B is the least count of the second scale and C is the least count when both the scales are used.

Let us now consider main scale and vernier scale combination say in vernier caliper as shown below:

Main scale is graduated in millimeter: this is a calibrated scale. The least count in this scale is 1mm. Vernier scale is such that its 10 divisions equal to 9 divisions on the main scale.
Thus one division of vernier scale is     9/10 mm=0.9mm.
The least count of the vernier scale is 0.9mm. The least count of vernier caliper is     1-0.9=0.1mm.

A vernier caliper in which the vernier scale is such that the 50 divisions on the vernier scale are equal to 49 divisions on the main scale. The least count of the vernier scale is  49/50 mm.

The least count of the vernier caliper is  1-49/50=0.02mm.

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