To Measure Internal Diameter and Depth of a Given Beaker Using Vernier Calipers and Finding its Volume

Dhristi JEE 2022-24

What are Vernier Calipers?

When you want to do length measurements with more accuracy and precision, you would need to use a piece of equipment called a sliding Vernier caliper. A Vernier caliper is used widely in laboratories and its main use is to measure diameters (both internal and external) of objects. 


On this page, we will look into the basics of a Vernier caliper, how measurements are marked on a Vernier caliper, some formulas around it, and finally, we will see how to measure the internal diameter and depth of a given beaker using Vernier caliper readings.


Parts of a Vernier Caliper

  1. The main scale is graduated in mm and cm and has two fixed jaws (A and C in the image below) which are projected at right angles to the scale.

  2. The sliding Vernier scale has two jaws, B and D, which are projecting at right angles to each other and also to the main scale. 

  3. There is a metallic strip E which, along with the jaw, is meant to measure the distance or diameter of objects.

  4. The knob (P) is used to slide the Vernier scale along the main scale and the screw (S) is used when you want to fix the position of the Vernier scale at the required position.


How Vernier Caliper is More Accurate than a Normal Scale?

For a common scale, the least count is 1 mm and it is not easy to further divide the least count of the scale to better its accuracy. With a Vernier scale, this can be achieved. When the jaws of the Vernier scale touch each other, the zero of both the main scale and the Vernier scale coincide. The high accuracy of a Vernier scale comes from the fact that there is a very small relative pitch difference between the two scales (main and Vernier).


The design of a Vernier caliper is such that the difference between each division on the Vernier scale is a fraction of the distance between divisions of the main scale. Usually, 10 small divisions on the Vernier scale are equal to 9 small divisions on the main scale. So, when the zero points of both the scales coincide, the Vernier scale’s first mark is 1/10th behind the main scale’s first mark, the second mark is behind by 2/10th, and so on. So this way it's only the 10th mark that coincides exactly on both the scales.


Hence, for any length, the division on the Vernier scale that coincides with the main scale gives us the difference of that division with the main scale. This is the principle behind the Vernier caliper measurement which lets us measure lengths in decimals.


The difference between the magnitudes of 1 MSD (main scale division) and 1 VSD (Vernier scale division) is referred to as the least count of the Vernier caliper. The least count is the smallest distance that can be measured by any measuring instrument.


\[n\times VSD = (n-1) \times MSD\]


Concept of Vernier Calipers

A caliper within them 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 caliper are adjusted to fit across the points to be measured and the caliper is then removed and the distance between the tips is measured using a ruler. 

 

The modern Vernier caliper 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 the 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.


The objective of Using Vernier Calipers

To measure the internal diameter and depth of a beaker/calorimeter using vernier calipers and hence finds its volume.


Parts of Vernier Calipers

A manual or traditional vernier caliper is an L-shaped measuring instrument with a movable arm. The movable arm is slid to adjust the object in between or around the jaws. A Vernier caliper has a total of four jaws, with two upper jaws used for measuring the internal distances and two lower jaws for measuring the internal distances of objects. Thus, the main parts of a vernier caliper are:

  •  Internal jaws

  • External jaws

  • Main arm

  •  Sliding arm

  • Depth measuring probe

  • Locking Screw


The Procedure of Finding Volume:

  • Determine and record the least count of the vernier caliper which is also known as the vernier constant.

  • To find the zero error, bring the movable jaw BD in contact with the fixed jaw AC. Repeat and record this three times. If there is no zero error, then record zero error as nil.

  • Now put the jaws C and D inside the beaker and open them till they make contact with the inner wall of the beaker without any pressure. Tighten the screw without putting too much pressure.

  • On the main scale, record the zero mark of the vernier scale. Just before the zero mark of the vernier scale, record the main scale reading which is known as main scale reading (M.S.R).

  • Let n be the number of the vernier scale division which coincides with the main scale division.

  • Rotate the vernier caliper 90° and repeat steps 4 and 5 for measuring the internal diameter in a perpendicular direction.

  • To measure the depth, find the total reading and zero correction.

  • The edge of the main scale of the vernier caliper should be placed on the peripheral edge. Care should be taken to make the strip go freely inside the beaker along with its depth.

  • Once the moving jaw of the vernier caliper touches the bottom of the beaker perpendicularly, the screw of the vernier caliper should be tightened.

  • For four different positions along the circumference of the beaker, repeat steps 4 and 5.

  • Find the total reading and also zero correction.

  • For internal diameter, take two different mean values and for depth, take four different values.

  • Calculate the volume using the proper formula and record the same in the result with units.

Formulas to Measure Internal Diameter and Depth of a Given Beaker

Below are some formulas that are used while taking measurements using a Vernier caliper:

  • Least count of Vernier caliper = \[ \frac{\text{magnitude of the smallest division on the main scale}}{\text{the total count of divisions on the Vernier scale}}\].

  • Final reading = Main scale reading + Vernier scale reading

  • Correction to compensate for zero error = Final reading - (+ Zero error)

  • 1 MSD = 1 mm = 0.1 cm

  • Total count of VSD (n) = 10

  • 10 VSD = 9 MSD

  • Vernier constant (VC) = 1 MSD - 1 VSD = (1 - 0.9) MSD = 0.1 MSD = 0.01 cm OR Vernier constant = \[\frac{1 MSD}{n} = \frac{1 mm}{10} = 0.01 cm\]

  • The volume of the beaker (same as the volume of a cylindrical hollow object),

\[ V = \pi \times r^{2} \times h = \frac{\pi \times D^{2} \times h}{4} \]; where D is the internal diameter of the beaker, r is its internal radius, and h is the internal depth.


How to Measure Internal Diameter and Depth of a Given Beaker Using Vernier Caliper

  1. Adjust the upper (A and B) of the Vernier caliper so that they touch the walls of the beaker from inside but do not exert pressure on it. 

  2. Now tighten the screws gently so that Vernier calipers are fixed in this position.

  3. Next, carefully note down the position of the zero mark on the Vernier scale against the main scale. It will not coincide exactly with the main scale division.

  4. Now take the main scale reading which is just to the left of the zero mark of the Vernier scale.

  5. Start looking through the Vernier window to find the reading on the Vernier scale which coincides exactly with a reading on the main scale (from the left end to the right end). Note down that reading, let us say it is n.

  6. Multiple “n” with the least count of the instrument and add this to the main scale reading which we found in step 3 above. Convert the result into proper units (usually it would be cm) so that the addition is valid.

  7. Repeat steps 3 to 6 for two different positions (angular) of the beaker.

  8. Keep the edge of the main scale of the Vernier caliper on its peripheral edge to determine the depth of the beaker. To do this make sure the tip of the strip is able to go down freely along with the depth of the beaker. 

  9. Keep sliding the jaw of the Vernier caliper till it touches the base of the beaker. While doing this ensure the jaws are exactly perpendicular to the bottom surface of the beaker. Once it reaches the bottom, tighten the screws of the Vernier caliper.

  10. Now repeat steps 4 to 6 to obtain the depth of the beaker. You must take the reading for depths at different positions of the beaker.

  11. Record your observations in a tabular format as shown below, making sure all units are proper and applying zero corrections if necessary.

  12. Find the mean of the corrected readings of the depth and the internal diameter of the beaker then express the results in suitable units and figures.

 

Dimension

Sr. No.

MSD in

 mm or cm

N (number of coinciding Vernier divisions)

VSD =

\[{n\times V_{c}}\]

in cm or mm

Measured diameter depth = MSD + VSD in

mm or cm

Internal Diameter D

1

2

3





Depth h

1

2

3





 

Mean diameter = ___ cm

Mean depth = ___ cm

Corrected diameter = ___ cm

Corrected depth = ___ cm

To know exactly how to measure the internal diameter of a given beaker, you will have to learn how to operate Vernier calipers. Learn from the top experts of Vedantu about how to use this instrument to take accurate measurements. Log on to the website to study the process elaborately.

FAQs on To Measure Internal Diameter and Depth of a Given Beaker Using Vernier Calipers and Finding its Volume

1. What is a Micrometer Screw Gauge?

Micrometer screw gauge is an instrument that can measure even smaller dimensions than a Vernier caliper. It uses an auxiliary scale (which can measure hundredths of an mm) marked on a rotary thimble. This instrument is a screw with an accurate and constant pitch (it is the magnitude by which the thimble moves backward or forward in one complete rotation). The thimble goes through a frame that has a scale in mm graduated to 0.5 mm. The small ratchet knob is used to rotate the thimble for adjusting the jaws. There is a friction clutch that prevents excessive tension from being applied. To open the jaws by 1 mm, the thimble needs to be rotated twice. To measure an object, it is placed between jaws, and using the ratchet the thimble is rotated till the object is secured in between.

2. Explain Negative Zero Error with an Example.

When the upper jaws of a Vernier caliper touch each other, the zero on the Vernier scale must coincide with the zero on the main scale. If this is not the case then the instrument is said to have a zero error. In negative zero error, the zero of the Vernier scale shifts to the left of the main scale when upper jaws touch each other. In a negative zero error, the readings taken are less than the actual reading which needs a correction to be applied in proportion to the left shift of zero on the Vernier scale. In the image above we can see that the 5th Vernier scale reading is coinciding with the main scale reading. So, the zero error here is: Zero error = \[5 \times {\text{least count}} = 5 \times 0.01 cm = 0.05 cm\].

3. Can you measure inner dimensions with a vernier caliper?

Vernier calipers can measure internal dimensions using the uppermost jaws in the picture at right, external dimensions using the pictured lower jaws, and depending on the manufacturer, depth measurements by the use of a probe that is attached to the movable head and slides along the center of the body. This probe is slender and can get into deep grooves that may prove difficult for other measuring tools.

4. How many parts of the vernier caliper are there?

The metric vernier scale is divided into 50 equal parts. The measuring range of the vernier scale is usually 1mm, with each increment representing 0.02mm. On an imperial caliper with a main scale of 6 inches, the vernier scale is 0.6 inches long and is divided into 25 parts. Each increment has a length of 0.001 inches.

5. What is the difference between vernier caliper and micrometer?

The main difference between a vernier caliper and a micrometer is that the vernier caliper uses two sliding scales with different spacing between markings on each scale while a micrometer makes use of a screw to translate small distances moved by its jaws to larger distances along the marked scale.

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