Physics Practicals Class XI
Vernier Callipers [Principle , Volume Of Sphere & Cylinder]Measurement Of Length :
Experiment 1 (a) : Vernier Caliper Basics
Vernier Calipers (Principle & Description)
Our Objective
- To know the use of the Vernier Calipers.
- To measure the diameter of a small spherical / cylindrical body.
- To measure the length, width and height of the given rectangular block.
- To measure the internal diameter and depth of a given beaker/calorimeter and hence find its volume.
The Theory
What is a Vernier Caliper?
A calliper is a device used to measure the distance between two opposing sides of an object. It can be as simple as a compass with inward or outward-facing points. First the tips of the calliper are adjusted to fit across the points to be measured and the calliper is then removed and the distance between the tips is measured using a ruler. The modern Vernier calliper was invented by Joseph R. Brown in 1851. It was the first practical tool for exact measurements that could be sold at an affordable price to ordinary machinists. The Vernier Calliper consists of a main scale fitted with a jaw at one end. Another jaw, containing the vernier scale, moves over the main scale. When the two jaws are in contact, the zero of the main scale and the zero of the Vernier scale should coincide. If both the zeros do not coincide, there will be a positive or negative zero error.
Parts of a Vernier Caliper
1.Main Scale
The main scale consists of a steel metallic strip graduated in centimeters at one edge and in inches at the other edge . It carries the inner and outer measuring jaws. When the two jaws are in contact, the zero of the main scale and the zero of the Vernier scale should coincide. If both the zeros do not coincide, there will be a positive or negative zero error.
2. Vernier Scale
A vernier scale slides on the strip. It can be fixed in any position by the retainer. On the Vernier scale, 0.9 cm is divided into ten equal parts.
3. Outer Measuring Jaws
The outer measuring jaws helps to take the outer dimension of an object
4. Inner Measuring Jaws
The inner measuring jaws helps to take the inner dimension of an object.
5. Retainer
The retainer helps to retain the object within the jaws of the Vernier calipers.
6. Depth Measuring Prong
The depth measuring prong helps to measure the depth of an object.
Least Count
The least count or the smallest reading which you can get with the instrument can be calculated as; 
or 
First calculate the least count and only then place the object between the two jaws. Record the position of zero of the Vernier scale on the main scale.
Calculating the Reading
When a body is between the jaws of the Vernier Caliper; If the zero of the vernier scale lies ahead of the Nth division of the main scale, then the main scale reading (MSR) is; 
If nth division of Vernier scale coincides with any division of the main scale, then the Vernier scale reading (VSR) is; 
Total reading, 
Finding the Volumes
Volume of a Beaker / Calorimeter
Volume of the beaker / calorimeter = internal area of the cross section x depth This can be expressed as; 
where 'D' is the internal diameter of beaker / calorimeter and 'd' the depth of beaker / calorimeter.
Volume of a Sphere
where 'r' is the radius of the sphere.
Volume of a Rectangular Block
where 'l' is length of the block, 'b' the breadth and 'h' the height of the block.
Learning Outcomes
- Students get to know the use of vernier calipers.
- Students know what is the Least count of vernier callipers.
Viva-Voce [Vernier Caliper Basics]
For: Physics Class 11
Q.1: What is the vernier callipers?
Ans. It is the simple instrument by which length of an object can be measured accurately up to one-tenth of a millimetre or one-hundredth of a centimetre.
Q.2: What is the use of Vernier Scale?
Ans. To increase the accuracy of the main scale.
Q.3: What is the least count (L.C.)?
Ans. The minimum measurement that can be taken by an instrument.
Q.4: What is the least count of
(a) meter scale (b) Stop Watch (c) Vernier
Ans. The least count of:
(a) meter scale = 0.1 cm or 1 mm.
(b) stopwatch = 0.01 sec or 1/100 sec. or according to the stopwatch.
(c) vernier scale = 0.01 cm or 0.1 mm
Q.5: What are the units of the vernier scale?
Ans. Vernier has no units of its own.
Q.6: What is the difference in the measurement of one smaller division on the main scale (M.S.) and that of vernier scale (V.S.)? Ans. (1 smallest Div. on M.S.) – (1 smallest Div. on V.S) = 0.1 – 0.09 = 0.01 cm = Least count.
Q.7: How the L.C. of a vernier is determined?
Ans. By using the relation: L.C. = (the Smallest division on Main Scale ) / (Total number of divisions on Vernier Scale) Q.8: Will the accuracy of a vernier will increase or decrease if 20 divisions are made in the same length? Ans. The accuracy will increase since the L.C. will decrease i.e. Accuracy α = 1 / Least count
Q.9: Which one is smaller M.S. div. or V.S. div.?
Ans. V.S. division.
Q.10: 1 division on V.S. = _____ cm.
Ans. 0.09 cm. 10 div. on V.S. = 0.9 cm 1 div. on V.S. = 0.9/10 cm = 0.09 cm
Q.11: What are the functions of (a) Sliding strip (b) Upper jaws ?
Ans. (a) For measuring depth. (b) For measuring the inner diameter.
Q.12: What is meant by zero error (Z.E.)?
Ans. The error which arises when zeros of M.S. and V.S. do not coincide upon joining the two jaws.
Q.13: When Z.E. is positive?
Ans. The Z.E. is positive when the zero of V.S. is to the right of the zero of M.S.
Q.14: How we find the corrected reading?
Ans. Corrected reading = Meaning reading – ( + Z.E.)
Q.15: Do you know any use of vernier scale?
Ans. It is used in the spectrometer, barometer, travelling microscope, etc.
Q.16: What are the significant figures?
Ans. Numbers 0, 1, 2, 3, ……. are called significant figures when they occur. The zero is not a significant figure if it is at the extreme left or extreme right of a number, e.g. 1.02 has three significant figures, but 1.20 has two significant figures.
Q.17: What is meant by the degree of accuracy?
Ans. It is the measurement estimated by the number of significant figures in the result.
Q.18: Why is the vernier callipers so-called?
Ans. A French mathematician named Pierre Vernier invented it and it is named after him.
Q.19: How does temperature affect the length of a cylinder?
Ans. The length of a cylinder increases with the increase of temperature and decreases with the decrease of temperature.
Q.20: What is the unit of volume?
Ans. In the MKS system, the unit of volume is m3. In the CGS system, the unit of volume