• Written By Amruta_D

# Measuring Diameter with Vernier Calipers: Virtual Lab Experiment

What are Vernier Calipers?

Vernier Calipers are precision instruments that can measure linear dimensions with a resolution from the tenth to the hundredth of a millimetre. The precision of a vernier caliper is hence a hundred times more than a nominal measuring scale which is precise up to a unit of a millimetre. In other words, the observed measurement from a measuring scale may read 72 mm or 50 mm, while a vernier calliper may measure 72.1 mm or 50.24 mm for the same objects, respectively. The instrument got its name from its inventor, French mathematician Pierre Vernier and its jaw-like design (callipers), which it utilises to hold the material whose dimensions are to be measured.

Diagram of Vernier Caliper

## What is the Least Count of Vernier Caliper?

In its modern form, a vernier caliper consists of a fixed main scale ( the conventional measuring scale with a precision of 1 mm), a sliding vernier scale which has markings for additional precise readings, four jaws or calipers to grab an object, and a tail to measure depths and heights.

The least count of an instrument is the smallest measurement that can be made using that instrument. For a Vernier Calliper, the least count is defined as the smallest distance it can measure accurately. There are two methods for measuring the least count.

Vernier Calliper Least Count Theory Video

Method 1

In this method, the least count is calculated by taking the ratio of the length of the smallest division on the main scale to the total number of divisions on the Vernier scale.

Mathematically. Least count= Length of 1 main scale divisionTotal number of divisions on vernier scale

Here, the value of the smallest division on the main scale is 1 mm, and the total number of divisions on the Vernier scale is 50. Therefore, the LC becomes 0.02 mm or 0.002 cm.
Note: This method is applicable only when the length of “n” Vernier scale divisions is equal to that of “n-1” main scale divisions.

Method 2

In this method, the least count is the difference between the lengths of one main scale division and one Vernier scale division. Mathematically, LC = 1 MS division – 1 VS division

In given example, 50 divisions of vernier scale coincide with 49 divisions of the main scale hence,
Length of 50 Vernier scale divisions =Length of 49 Main scale divisions

Length of 1 Vernier scale division=Length of 4950Main scale division

LC = 1 MS division – 1 VS division

LC = 1mm – (4950) mm

LC = 1mm – 0.98 mm

Therefore, LC    = 0.02 mm

Linear dimensions like radius, diameter, length, breadth and height etc, can be measured using a vernier caliper. Let us discuss the steps to measure the diameter of a cylindrical object.

Step – 1: Fix the sphere between the lower jaws of the Vernier caliper.

Since we are measuring the diameter of a sphere we will fix the sphere between the lower external jaws. To do this we move the movable jaws by loosening the locking screw and then tightening it once the object is perfectly grabbed between the jaws.

Observe the zero of the Vernier scale. If the zero of the Vernier scale is coinciding with one of the divisions of the main scale, that particular division is the main scale reading. If it does not coincide, the division of the main scale which is just to the left of the zero of the Vernier scale will be the reading of the main scale.

Here, the zero of the Vernier scale lies exactly after the 25 mm mark so the main scale reading will be 25 mm.

Step – 3: Read the Number of the coinciding Vernier division

Next, we need to observe the division of the Vernier scale that almost coincides with any of the divisions of the main scale; this division of the Vernier scale after multiplying with the least count will give the Vernier scale reading.

In our case, the number of divisions on the Vernier scale which coincides with the main scale division is 31.

Step – 4: Calculate the Vernier scale reading

The Vernier scale reading is equal to the Least count multiplied by the number of the coinciding Vernier division.

So, in this case, the Vernier scale reading will be 0.02 mm multiplied by 31, equaling 0.62 mm.

Step – 5: Calculate the Diameter of the sphere

The diameter or the measured reading will be calculated as the Main scale reading plus Vernier scale reading

= 25 mm + 0.62 mm

= 25.62 mm

What is Zero Error in Vernier Caliper?

Zero error – When the two jaws are in contact with each other, the zero of the Vernier scale should coincide with the zero of the main scale. The Vernier calliper is said to have a zero error if it does not coincide. There are two types of zero errors possible in the instrument.

Positive zero error – If the zero of the Vernier scale is to the right side of the zero of the main scale, then the Vernier calliper is said to have a positive zero error. If a Vernier calliper has a positive zero error, the length measured by it will be more than the actual length.

Negative zero error – If the zero of the Vernier scale is to the left side of the zero of the main scale, then the Vernier calliper is said to have a negative zero error.  If a Vernier calliper has a negative zero error, the length measured by it will be less than the actual length.

Vernier Calliper Zero Error Theory Video

To obtain an accurate measurement, zero error correction must be applied. The zero error value must be subtracted from the final reading to obtain the correct length. Hence, Actual length=Measured length -zero error.

Applications of Vernier Calipers

A vernier calliper provides an added degree of precision and hence is used for this purpose in almost all industrial and scientific areas. Some of them are listed below.

• Automotive – Safety requirements in automotive applications are high, and a perfect fitting of components requires high precision measurements. Given its order of precision, a vernier calliper proves to be a handy instrument in gauging the assembly tolerance in automotive parts. For the same purpose, it is used in Aeronautics, construction and every other industry with an assembly line of components.
• Fine metal work – Metalwork often requires the order of precision in measurements as offered by a vernier calliper. For the same reason, a vernier calliper finds high popularity among fine metal workers like Goldsmith, Locksmith, etc.
• Science laboratories. Many scientific research and investigations require an order of precision as that of a vernier scale. For example – In Palaeontology, Meteorology, Classical Mechanics, etc.
• Carpentry – Carpentry jobs, especially in creative applications, a vernier calliper finds itself to be a useful precision instrument.

Solved Examples for Vernier Calipers

Anshul Jajoo There are no sentences preceding the solved examples. Also, put the solved examples in paragraphs and not a table.

Here are some solved examples. Based on what you learned above, try answering these on your own.

Solved Example-1: If the length of 1 main scale division equals 1 mm, what is the least count for the shown Vernier calliper?

1. 0.14 mm
2. 0.3 mm
3. 0.1 mm
4. 0.15 mm

Solution:

Least count=1MSD-1VSD

10 VSD=7 MSD

1VSD=0.7MSD=0.71mm=0.7mm

Least count=1MSD-1VSD=0.3mm

Solved Example-2:  An object whose diameter is to be measured is fixed between the jaws of a Vernier calliper. Consider the Vernier calliper to be a conventional Vernier calliper having the least count = 0.1 mm and 1 MSD = 1 mm. The scale looks as shown in the figure below.

2.1 The main scale reading is

1. 10 mm
2. 9 mm
3. 11 mm
4. 1 mm

Solution: The division of the main scale that is just left to the zero of the Vernier scale is 9 mm.

2.2 The Vernier scale division that coincides with the main scale division is

1. 5
2. 4
3. 3
4. 9

Solution: The division of the Vernier scale that coincides with one of the main scale divisions is 5.

2.3 The measured value of the diameter is

1. 10.5 mm,
2. 9.2 mm,
3. 9.5 mm,
4. 9.6 mm

Solution

(Least countNumber of coinciding division on Vernier Scale)

Measured diameter= 9 mm+(0.1mm5) =9.5 mm

Vernier Calliper Experiment

Experiment Title – Use of Vernier Callipers to Measure Diameter

Experiment Description – In this experiment, we will dive deep into understanding Vernier Callipers, and measure the diameter of a spherical/cylindrical object using one.

Aim of Experiment – Use Vernier Callipers to measure the diameter of a small spherical/cylindrical body

Material Required – Vernier Callipers, Spherical Object and Cylindrical Object

Procedure –

Steps for measuring the diameter of a sphere using a vernier callipers are –

1. Calculate the least count
2. Fix the object between the lower jaws of the vernier callipers
3. Note the main scale reading
4. Read the number of the vernier division coinciding with a main scale division
5. Calculate the vernier scale reading by multiplying the coinciding vernier scale division with the least count
6. Measure the diameter using the formula (Main scale reading) + (Least count x Number of coinciding vernier division)
7. Remove the object from the jaws of vernier callipers. And slide the vernier scale such that the two jaws are touching each other
8. If the main scale’s zero coincides with the vernier scale’s zero, there is no zero error. But if they are not coinciding, there is a zero error
9. Repeat steps 3 to 6 to calculate the zero error
10. Subtracting zero error from the measured diameter will give the correct diameter

Precautions –

1. If the Vernier scale is not sliding smoothly over the main scale, apply some machine oil/grease
2. Screw the Vernier tightly without exerting undue pressure to avoid any damage to the threads of the screw
3. Keep your eye directly over the division mark to avoid any error due to parallax
4. Note each observation with correct significant figures and units

FAQs on Vernier Calipers

Q1. Do all vernier callipers available in the market have the same least count?

Ans: No. All the vernier callipers don’t have the same least count. The least count of a vernier calliper depends upon an instrument’s total length of the vernier scale. However, an instrument maker generally provides the detail of the least count with it. It may vary from the tenth part of a millimetre to a hundredth part.

Q2. Before starting the experiment, should we always check for zero error in a vernier calliper?

Ans: Yes. A zero error is an instrumental error with a significant probability of being present, if not high. So it is always advised to check for zero error to get an accurate result.

Q3. Is being more precise the same as being more accurate?

Ans: No. Precision and accuracy have different meanings. While precision means being closer and closer to a certain value, accuracy means being close to the true value. Accuracy depends upon the errors in the measurement of which precision is one of the factors.

Q4. Is a vernier calliper the most precise instrument available to measure linear dimensions?

Ans: No. A screw gauge can measure up to the thousandth part of a millimetre. Hence it is also called a micrometre.

Q5. Is a vernier calliper easily available?

Ans: Yes. Of all the measuring instruments, a vernier calliper is among the most popular. You can easily find it in engineering and scientific laboratories or stores that trade in lab equipment if not in your local stationary stores.

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