Step-by-Step Guide to Precision Measurement in Physics Experiments
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
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.
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.
There is a metallic strip E which, along with the jaw, is meant to measure the distance or diameter of objects.
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
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.
Now tighten the screws gently so that Vernier calipers are fixed in this position.
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.
Now take the main scale reading which is just to the left of the zero mark of the Vernier scale.
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.
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.
Repeat steps 3 to 6 for two different positions (angular) of the beaker.
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.
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.
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.
Record your observations in a tabular format as shown below, making sure all units are proper and applying zero corrections if necessary.
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.
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 How to Measure Internal Diameter, Depth, and Volume of a Beaker Using Vernier Calipers
1. What are the essential parts of a Vernier caliper used to measure a beaker's dimensions?
To measure a beaker's internal diameter and depth, you will primarily use four parts of the Vernier caliper:
- Internal Jaws: The smaller, outward-facing jaws at the top, designed to fit inside an object to measure its internal dimensions.
- Main Scale: The fixed scale along the body of the caliper, usually marked in millimetres (mm) and centimetres (cm).
- Vernier Scale: The small sliding scale that moves along the main scale to provide high-precision fractional readings.
- Depth Rod: A thin rod that extends from the end of the main scale as the slider moves, used for measuring the depth of holes or steps.
2. How do you correctly measure the internal diameter of a beaker using a Vernier caliper?
Follow these steps to measure the internal diameter:
- First, check for any zero error by closing the jaws completely.
- Insert the internal jaws into the beaker.
- Gently slide the movable jaw outwards until both jaws lightly touch the inner walls of the beaker. Ensure the jaws are perpendicular to the beaker's axis.
- Tighten the locking screw to fix the reading.
- Read the Main Scale Reading (MSR), which is the mark on the main scale just to the left of the zero on the Vernier scale.
- Find the Vernier Scale Coincidence (VSC), which is the mark on the Vernier scale that aligns perfectly with any mark on the main scale.
- Calculate the diameter using the formula: Total Reading = MSR + (VSC × Least Count). Remember to apply the zero correction if any.
3. What is the procedure for measuring the internal depth of the beaker with a Vernier caliper?
To measure the internal depth, use the depth rod of the Vernier caliper. Rest the bottom edge of the main scale firmly on the top rim of the beaker. Carefully slide the movable jaw downwards until the depth rod just touches the bottom surface of the beaker. The reading is taken in the same way as the diameter, by combining the Main Scale Reading and the Vernier Scale Coincidence.
4. Once the internal diameter and depth are measured, what is the formula to find the beaker's volume?
A beaker is treated as a cylinder for this calculation. The formula for the volume (V) of a cylinder is:
V = πr²h
Where:
- r is the internal radius of the beaker (Internal Diameter / 2).
- h is the internal depth of the beaker.
- π (pi) is a constant, approximately equal to 3.14159.
Ensure you use the corrected values of diameter and depth after accounting for any zero error.
5. What is zero error in a Vernier caliper and how does it impact the final volume calculation?
Zero error occurs when the zero mark of the Vernier scale does not coincide with the zero mark of the main scale when the jaws are fully closed. It can be positive (Vernier zero is to the right) or negative (Vernier zero is to the left). This error must be corrected from every measurement taken. If ignored, the measured diameter and depth will be inaccurate, leading to a significant error in the calculated volume, as the volume depends on the square of the radius.
6. Why is it standard practice to take multiple readings for both the diameter and depth?
Taking multiple readings and calculating the average is crucial for accuracy. A beaker may not be a perfectly uniform cylinder; its diameter might vary slightly at different points, and its base may not be perfectly flat. By measuring the diameter at different orientations and the depth at different points, you can calculate a mean value that better represents the beaker's true average dimensions, thereby minimising random errors and improving the reliability of the final volume.
7. Why do we specifically use the *internal* diameter, not the external, to calculate the beaker's holding capacity?
The objective is to find the volume of substance the beaker can hold, which is its internal capacity. The internal diameter defines the space available inside. Using the external diameter would incorrectly include the volume of the glass walls, giving you the total volume occupied by the beaker itself, not its capacity. Therefore, for finding how much liquid it can contain, the internal dimensions are essential.
8. What is the basic principle that allows a Vernier caliper to be more precise than a standard ruler?
The high precision of a Vernier caliper comes from its least count, which is the smallest measurement it can accurately make. This is achieved by the clever use of two different scales. The divisions on the sliding Vernier scale are slightly smaller than the divisions on the main scale. The principle is based on the alignment of these scales; the difference in size between one main scale division and one Vernier scale division gives the least count, typically 0.01 cm, allowing measurement of a fraction of a millimetre.
9. What are the most common practical mistakes to avoid during this experiment?
To ensure accurate results, students should avoid these common errors:
- Parallax Error: Not keeping your eye directly perpendicular to the scale while taking a reading.
- Excessive Pressure: Applying too much force with the jaws, which can compress or distort the object or the caliper itself.
- Ignoring Zero Error: Forgetting to check for and apply the zero correction, which leads to systematic errors in all measurements.
- Incorrectly Identifying VSC: Misjudging which Vernier scale line is perfectly coinciding with a main scale line.
10. Could you use this same method to find the internal volume of a hollow metal pipe?
Yes, absolutely. The method is versatile for any hollow cylindrical object. For a pipe, you would use the internal jaws of the Vernier caliper to measure its internal diameter and the depth rod to measure its length (which serves as its 'depth' or 'h'). The same volume formula, V = πr²h, would then be applied to find the internal volume of the pipe.
