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2 questions have been asked in JEE-Main and 3 in JEE-Advanced on this concept in last 10 years.
The measurement of length is necessary in almost all the experiments in Physics. There are experiments where greater accuracy is not required. In such experiments, a meter scale is used to measure distances correctly up to a millimetre. To measure a length correctly up to a fraction of a millimetre, the division must be subdivided. Hence, a meter scale cannot be used in measurements that requires greater accuracy. For accurate measurement up to or of a millimetre, there are various devices that can be used, such as
(A) Vernier caliper (B) Screw gauge
(I) Vernier caliper:-
A Vernier caliper consists of a rectangular steel bar such that inch is marked on one edge and centimetre is on the other edge, as shown in the figure below.
It consists of a main scale and over the main scale slides a small scale called the Vernier scale.
The instrument has two jaws A and B. Jaw A is fixed while the other jaw B can slide over the main scale. Screw S is used to fix the moveable jaw at any position. Some Vernier calipers have two extra jaws P and Q, which are used to measure the internal diameters of hollow objects.
Least count:
The smallest value that can be measured by a measuring instrument is called its least count. It is easy to determine the least count of a main scale, but to determine the least count of a Vernier scale is tricky.
Consider a Vernier scale with 10 equal divisions. Let these 10 equal divisions coincide with 9 of the main scale divisions, as shown in the figure.
The difference between one main scale division (MSD) and one Vernier division (VD) is called the Vernier constant or the least count of the Vernier.
Suppose that while taking the measurement of a small object, the zero of the Vernier scale lies between 1.2 and 1.3 as shown in the figure below.
The 6th Vernier division coincides with the scale division. Let the fraction after 1.2 be x.
Substitute the known values from equation (1).
Therefore, the reading now becomes 1.26 MSD. This shows the precision of Vernier calipers.
In general, if n Vernier divisions are equal to scale divisions, the least count of the scale is written as
The total reading of a Vernier scale can be found using the following formula
Here,
N = main scale reading before on the left of zero of the Vernier scale
n = number of Vernier scale division which just coincide with any of the main scale division
(B) Screw gauge:
It is based on the principle of a screw and consists of a U-shaped frame F with a fixed end at A. A fine and accurately-cut screw passes through the other end B. The head scale or the circular scale is used to measure the fraction of revolution. The number of complete revolutions can be read on the pitch scale S. The reading of the circular scale is taken against a reference line. The screw gauge is provided with a rachet arrangement R. When jaws A and C are in contact with each other or with some other object placed between them, the rachet slips and the screw stops moving forward.
A screw gauge is used to accurately measure wires of small thicknesses or diameters instead of using a meter scale. To find the diameter of a wire, insert the wire between the jaws and turn the cap till the wire is just held between them without any pressure.
Pitch:
The pitch of a screw can be measured in the following manner.
(i) Rotate the circular scale and coincide the zero mark with the reference line. Note the reading on the pitch scale.
(ii) Give four complete rotations to the circular scale and note the reading on the pitch scale again.
(iii) The formula to calculate pitch is
Least count:
The formula for the least count of a screw gauge is
Zero correction:
If both the jaws are brought in contact with each other, the zero of the circular scale may not coincide with the reference line. In such cases, there is a zero error.
To find the zero correction, count the number of divisions on the circular scale by which the zero mark has advanced beyond or is left behind the reference line. Multiply this number with the least count. This is the zero correction. If the zero of the circular scale has advanced beyond the reference line, the zero correction is positive; however, if it is left behind the reference line, it is negative.
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