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Vernier Calipers are instruments for calculating precise linear measurements. It determines the linear distance between two points.
- The tips of the caliper are first adjusted to fit across the points to be measured, after which the caliper is removed and the distance between the tips is measured with a ruler.
- Pierre Vernier of France developed the Vernier Calliper in 1631. It was created as a tool for determining highly accurate linear measures.
- A vernier caliper includes two graded scales: one for the primary scale and one for the auxiliary scale.
- This scale moves parallel to the main scale and delivers readings in fractions of a division.
- The vernier constant, also known as the least count of vernier calipers is defined as the difference between one main scale division and one vernier scale division.
- The case in which the measuring instrument records a reading when there should be no reading is referred to as zero error.
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Key Terms: Vernier caliper, Vernier constant, Least count, Zero error, Least count error, Vernier scale, Measuring instrument, Magnifying glass
Aim
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To measure the internal diameter and depth of a beaker using vernier calipers and find the volume.
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Apparatus Required
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The apparatus required for this experiment are
- A Vernier caliper
- A cylindrical object like a beaker
- A Magnifying glass
Theory
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A caliper is a device used to measure the distance between two opposing sides of an object. It can be as simple as a compass with points pointing inside or outward. The caliper's tips are first adjusted to fit across the locations that need to be measured, then the caliper is removed and the distance between the tips is measured with a ruler.
Least Count
The least count of a measuring instrument is the smallest value in the quantity measured that can be resolved on the instrument's scale.
- The least count is related to the precision of an instrument.
- An instrument that is capable of recording smaller changes in a value relative to another instrument has a lower "least count" value and is therefore more accurate.
- Any measurement made by the instrument can be considered repeatable to no less than the resolution of the least count.
- The least count of an instrument is inversely proportional to the precision of the instrument.
Calculation of Least Count
The least count of a vernier caliper is given by
\(LC = \frac{Fraction magnitude of the smallest division on the main scale}{ Total number of small divisions on the vernier scale}\)
The formula used to calculate the volume of the beaker is given by
V = \(\pi (\frac{D}{2})^2d\)
Where
- D is the internal diameter of the beaker
- d is the depth of the beaker
Diagram
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Depth of Beaker
The internal diameter of the beaker
Procedure
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The following steps should be taken to measure the internal diameter, depth, and volume of the beaker
- Step 1: Find and record the least count of the vernier caliper, commonly known as the vernier constant.
- Step 2: Bring the moveable jaw BD into contact with the fixed jaw AC to determine the zero error. This should be done three times. If there is no zero error, then zero error is recorded as nil.
- Step 3: Insert jaws C and D into the beaker and open them until they make contact with the inside wall of the beaker. Tighten the screw without using too much force.
- Step 4: Record the zero mark of the vernier scale on the main scale. Record the main scale reading, often known as the main scale reading (M.S.R), just before the zero mark of the vernier scale.
- Step 5: Let n be the number of the vernier scale division that corresponds to the main scale division.
- Step 6: To measure the interior diameter perpendicularly, rotate the vernier caliper 90° and repeat steps 4 and 5.
- Step 7: Find the total reading and zero correction to determine the depth.
- Step 8: The edge of the main scale of the vernier caliper should be placed on the peripheral edge. It is important to ensure that the strip can move freely inside the beaker and that its depth is proper.
- Step 9: When the movable jaw of the vernier caliper meets the bottom of the beaker perpendicularly, tighten the vernier caliper screw.
- Step 10: Repeat steps 4 and 5 for four different points around the perimeter of the beaker.
- Step 11: Determine the total reading as well as the zero correction.
- Step 12: Take two different mean values for internal diameter and four distinct mean values for depth.
- Step 13: Calculate the volume using the appropriate formula and note the result in units.
Observations
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The following are the observations of the experiment
- For the determination of the least count of vernier caliper, we have
1 M.S.D = 1 mm
10 V.S.D = 9 M.S.D
Where MSD refers to the main scale division and VSD refers to the vernier scale division
Therefore 1 V.S.D = 9/10 M.S.D = 0.9 mm
The least count of vernier caliper (V.C) = 1 M.S.D – 1 V.S.D = (1-0.9) mm = 0.1 mm = 0.01 cm
- Zero error = (i)…. cm, (ii)…. cm, and (iii)…..cm
Mean zero error (e) = …..cm
Mean zero correction (C) = -(e) = …….cm
- Table for internal diameter (D)
| S. No. | Main scale | Vernier Scale Reading | Total Reading | ||
|---|---|---|---|---|---|
| No. of vernier division coinciding (n) | Value [n×(V.C)] | Observed D0 = N + n × V.C | Corrected D = D0 + C | ||
| 1. | D1 = | ||||
| 2. | D2 = | ||||
| 3. | D3 = | ||||
| 4. | D4 = | ||||
- Table for depth (d)
| S. No. | Position | Main scale | Vernier Scale Reading | Total Reading | ||
|---|---|---|---|---|---|---|
| No. of vernier division coinciding (n) | Value [n×(V.C)] | Observed d0 = N + n × V.C | Corrected d = d0 + C | |||
| 1. | at A | d1 = | ||||
| 2. | at B | d2 = | ||||
| 3. | at C | d3 = | ||||
| 4. | at D | d4 = | ||||
Calculations
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Mean corrected internal diameter
D = \(\frac{D_1(a) + D_1(b)}{2}\) = .......... cm
Mean correction depth
d = \(\frac{d_1 + d_2 + d_3 + d_4}{4}\) = .......... cm
The volume of the beaker
V = \(\pi (\frac{D}{2})^2d\) = .......... cm
Result
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The volume of the beaker is …….cm3
Precautions
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Following precautions should be taken while performing the experiment
- To help the vernier scale move smoothly over the main scale, apply machine oil or grease.
- To avoid thread damage, do not apply much pressure to the vernier screw.
- Keep the eye directly above the dividing mark to avoid parallax errors.
- The units and significant figures used in observations must be accurate.
Sources of Error
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The errors can be introduced in the measurement due to the following reasons
- Not taking into consideration the zero error in the instrument.
- Avoid gaps and excessive pressure while positioning vernier calipers.
Things to Remember
- A vernier caliper is a measuring equipment that is used to take extremely precise linear measurements.
- The vernier scale functions on the principle that the number of vernier scale divisions that coincide with the main scale division should be either one less or one more.
- The least count is the lowest value that can be measured using a measuring instrument.
- The least count of the vernier caliper is also known as the vernier constant.
- It is the difference between the values of one main scale division and one vernier scale division.
- The condition in which a measuring device records a measurement when no reading is required is referred to as zero error.
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Sample Questions
Ques. What do you mean by Vernier constant? (2 Marks)
Ans. The difference between the values of one main scale division and one vernier scale division is defined as the vernier constant.
The vernier constant is also known as the least count of the vernier caliper, which is the shortest length that can be correctly measured with this instrument.
Ques. What is Vernier Calliper? (2 Marks)
Ans. A vernier caliper is a measuring instrument used for measuring linear measurements with extreme precision. It may also be used to measure the diameters of circular objects using the measuring jaws.
Ques. What is meant by a measuring tool? (1 Mark)
Ans. Measuring tools are equipment used to count measurements about a body, such as length, temperature, height, breadth, and so on.
Ques. What are the main examples of measuring tools? (2 Marks)
Ans. The main examples of measuring tools are
- Vernier calipers
- Screw gauges
- Rope gauges
- Dial gauges
- Rulers
- Sheave gauge
Ques. What is meant by least count (L.C.)? (1 Mark)
Ans. The lowest value that can be measured using a measuring device is specified as the least count.
Ques. Which is more accurate a vernier caliper or a screw gauge? (2 Marks)
Ans. A screw gauge is a more precise measuring device than a vernier caliper since the vernier caliper's least count is 0.1 mm and the screw gauge is 0.01 mm.
Ques. What is the use of sliding jaws of vernier calipers? (1 Mark)
Ans. The use of sliding jaws of vernier calipers is to measure the diameter of a sphere.
Ques. What is the principle behind the vernier scale? (2 Marks)
Ans. The vernier scale functions on the principle that the number of vernier scale divisions that coincide with the main scale division should be either one less or one more.
Ques. What are the uses of a Vernier caliper? (3 Marks)
Ans. The uses of a vernier caliper are
- Vernier calipers are tools for measuring the length of a rod or any other object.
- Vernier calipers are useful for determining the diameter of a sphere.
- Vernier calipers are also used to determine the outside and inside diameters of a hollow cylinder, as well as the depth of a small beaker.
Ques. What do you mean by systematic error? (2 Marks)
Ans. Errors that occur in one direction, whether positive or negative, are known as systematic errors. Personal mistakes occur as a result of poor instrument configuration, and so fall under the category of systematic error.
Ques. What is the range of the Vernier caliper? (2 Marks)
Ans. The difference between the largest and smallest measurement readings determines the maximum capacity of a vernier caliper. Typically, it is the total length of the main scale of the vernier caliper. The normal range of vernier calipers is 300 mm.
Ques. Using a scale, can you measure the diameter of a thread? (3 Marks)
Ans. Yes, the diameter of the thread may be measured by winding it on a meter scale with its turns close together. The number of turns completed by the thread is then recorded as well as the thickness of the thread coil. Now, divide the entire thickness of the wound by the number of rotations to get the diameter.
Ques. What is the least count of a screw gauge? (2 Marks)
Ans. The least count of a screw gauge is typically 0.001 cm or 0.01 mm, however, a micrometer can alternatively be used for more exact readings.
Ques. What is the difference between a vernier and a caliper? (2 Marks)
Ans. A caliper is a device used to measure the thickness of an object's two sides, whereas a vernier is a secondary scale with finer graduations (for more precise measurements) than the primary scale of a measuring instrument. The vernier scale gathers readings between the graduations of the larger scale.
Ques. What is the resolution of a vernier caliper? (2 Marks)
Ans. The resolution of a vernier caliper, also known as vernier reading is the smallest measurable distance that a vernier caliper can obtain.
Vernier calipers generally have a resolution of 0.001 inches, whereas metric vernier calipers have a resolution ranging from 0.02 mm to 0.05 mm.
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