Measure Diameter of a Small Spherical Body Using Vernier Callipers

Vernier caliper was invented by a French Mathematician named Pierre Vernier in 1631. It is an instrument for making very accurate measurements.

Vernier caliper works on the principle that vernier scale uses the alignment of line segments that can be displaced by small amounts for the measurement.

It uses two scales viz: the main scale and the auxiliary scale. The main is similar to the ruler, while the vernier scale slides on the main scale that makes readings to the fraction of a division on the main scale.

Vernier Caliper Measurement

Vernier calipers are used in the two following areas:

• In scientific laboratories.

• For quality control measurements.

Vernier calipers measure the diameter of small spherical objects, depth, and length very accurately, that’s why they are called Precision measuring instruments.

Parts of Vernier Caliper

A vernier caliper has the following parts:

1. Outside Jaws: To measure the external diameter of a small spherical object.

2. Inside Jaws: To measure the internal dimension of a small spherical object.

3. Measuring Depth Probe: For measuring the depth of objects.

4. Main Scale: In cm.

5. Main Scale: in inches.

6. Vernier Scales: In cm.

7. Vernier Scales: In inches.

8. Retainer: To block the movable part.

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The formula for the vernier caliper measurement is:

Measurement = MSR + (VSR * L.C.)

The least count of the vernier caliper is:

L.C.  measurement = 1 MSD - 1VSD

Objective: To ascertain the diameter of a spherical body.

Apparatus/Materials Required:

• Spherical object viz: a spherical marble piece, or a pendulum bob.

• Vernier Caliper.

• Magnifying glass.

Theory

The smallest distance that can be measured along with the distance is the least count or L.C. L.C.is the difference between one main scale division and one vernier scale division.

The formula for the same is given below:

n (MSD) = (n - 1) VSD

Here,

MSD = Main scale division.

VSD = Vernier scale division.

Measure Diameter of a Small Spherical using Vernier’s Calipers

Procedure to measure diameter of a small spherical cylindrical body using vernier’s calipers is as follows:

• Check with the instrument, keep both the jaws closed and make sure that the zero of the main scale and the vernier scale coincide with each other.

• Now, use a magnifying glass to check whether we were able to coincide the two zeroes and then check the number of divisions coinciding with each other.

• Release the movable jaw by opening the screw. Put the cylindrical spherical body inside these jaws but not tightly. Make sure that these jaws lie perpendicular to the body. Slowly and gently tighten the screw to adjust the instrument in the position of the body.

• Note the position of zero of the vernier scale against the main scale ( we won’t get the perfect coincide). Now, read the reading on the main scale division to the left of the zero marks of the vernier scale (V.S.).

• Find the precise coincidence of the main scale division with the vernier scale division in the vernier window, moving from the left end to the right and then note down number ‘M’.

• Multiply the least count of the instrument with the number ‘M’. Add the acquired product to the main scale reading noted in step 4. We need to make sure that the product so obtained is to be converted into proper units for addition.

• Now, repeat the steps from 3 to 6, do the measurements along with the different positions of the curved surface of the sphere, and obtain at least three readings in each case.

• Finally, record all the observations in a tabular form and apply the arithmetic mean of the correct readings of the diameter of the body.

What Did You Observe?

We observed the following things:

• Main scale 1 mm  = 0.1 cm.

• Number of vernier scale division (M) = 10.

• If 10 vernier scale divisions are equal to 9 main scale divisions, then:

1 vernier scale division is equal to 0.9 main scale divisions.

• Vernier constant  = 1 MSD - 1 VSD  = 1 - 0.9 = 0.1 main scale divisions

• So, we get the vernier constant as 0.1 MSD = 0.1 mm = 0.01 cm.

So, observed reading  - (± Zero reading) = True reading.

So, this was the procedure to measure the diameter of a small spherical. Now, record all the readings in the table given below:

The Table form for Noting the Details of Measuring the Diameter of a Small Spherical is:

Zero error = ± ……cm.

Mean observed diameter in cm = ……

The formula for the corrected diameter is the difference between the mean observed diameter and the zero error.

Our final result is:

The diameter of the cylinder or the sphere in…...cm.

Types of Vernier caliper

Flat Edge Vernier Caliper - This kind of vernier is used for basic tasks. We can measure the length, breadth, diameter and thickness of a task, among other things. Because the jib on its edge is of a unique kind, it may also be used to obtain the inner measurement. However, the job breadth must be deducted from that measurement.

Knife Edge Vernier Caliper - This Vernier caliper’s edge is as sharp as a knife. This vernier caliper is useful for measuring tiny spaces, the distance between bolt holes, and so on. Its basic flaw is that the thin edge of its jaw wears down fast, causing it to give incorrect measurements.

Vernier Gear Tooth Caliper - This is a unique tool that resembles the combination of two vernier calipers. It has two distinct scales, vertical and horizontal. The thickness of a gear tooth may be calculated using a vernier caliper and its pitch circle.

Vernier Depth Gauge - This tool is used to gauge the depth of a job's slot, hole, or groove. This depth gauge is created from a thin beam, similar to a narrow rule. It has an inch or metric system for the main scale and vernier scale. This is nearly identical to a vernier caliper. However, instead of a jaw, it has a flat-shaped base, as illustrated in the figure. 

Vernier Height Gauge - It's used to take accurate measurements of a job's height or to mark it. It's comparable to a vernier caliper, but it's utilized by connecting certain extra attachments to it. The length of the beam is still fixed to a base. The height of a task is measured or marked with an offset scriber mounted on the beam itself. 

Vernier Dial Caliper - When using a standard vernier caliper, there is a potential of making a mistake when it comes to clear reading. Vernier Dial calipers are now often used for this purpose. It has a graduation dial in place of the vernier scale, as indicated in the illustration. It can measure in both inches and millimetres, just as vernier calipers. Rack and pinion are employed in it, same as in a dial test indicator. The rack is still attached to the main scale, which is connected to the dial's pinion.

Precautions

When using a vernier caliper, take the following precautions into account:

• The parallax error is the most prevalent type of mistake. When an object is seen from a different angle, this mistake happens. This causes the object to look in a little different location than it actually is, which can cause us to misread a measuring scale. When taking the Main Scale reading and the Vernier Coincidence, the observer should place his eyes exactly above the scale to eliminate this inaccuracy. 

• While measuring, make sure to take all of your readings in the same unit system. If any measurements are collected in a different system's unit, they must be converted to the correct units before being utilized in calculations.

• When gripping the object to be measured, avoid using too much force on the jaws. The thing should be gently held between the jaws at all times.

• Make sure the vernier caliper does not have a zero error before taking any measurements. If the error is zero, the necessary connections should be made.

• Measuring precision is mostly determined by two senses:

• Sense of sight

• Sense of touch

• A cloth soaked in cleaning oil should be used to clean and dry the object's surface and instrument cover.

• Loosen the vernier caliper locking key and ensure there is no friction between the scales while rotating the vernier caliper’s jaws.

• Additional measures should be required in the case of a digital vernier caliper: Press the on/off button after bringing the jaws into contact with each other. 

1. Check the reading and make sure it is zero.

2. Move the slider and check whether all the buttons and the LCD display are working properly.