Experiment-Vernier calliper

  Experiment 1

AIM: To

(i) Determine the diameter of a small cylindrical or spherical body, 

(ii) Calculate the density of a given regular body by measuring its dimensions and mass,

(iii) Compute an object's volume by measuring the internal diameter and depth of a given cylindrical object, such as a beaker, glass, or calorimeter.

APPARATUS AND MATERIAL REQUIRED: 

Vernier Callipers , a cylindrical object like a beaker, glass, or calorimeter, a marble, a rectangular block of known mass, or a spherical body like a pendulum bob.

DESCRIPTION OF THE MEASURING DEVICE:

1)  Two scales make up a Vernier calliper: a main scale and a Vernier scale that glides along the main scale. Despite having smaller divisions of varying magnitudes, both the main scale and the Vernier scale have them.

Graduations on the main scale are in cm and mm. A and C, its two fixed jaws, are positioned so that they are perpendicular to the scale. The main scale, a metallic strip (N), and two jaws (B, D) that project at right angles are all present on the sliding Vernier scale. When the jaws are brought into contact with one another, the main scale and Vernier scale zeros coincide. Measurements of object distance and diameter are made possible by the metallic strip and jaws. The vernier scale on the main scale is moved using knob P. Screw S is used to fix the vernier scale at a desired position.

VERNIER CALLIPER

2) A typical scale has a count as low as 1mm. It is challenging to further divide it in order to raise the scale's lowest count. This is made possible with the aid of a vernier scale.

PRINCIPLE:

The instrument's "least count" refers to the lowest distance that can be measured using it, which is the difference between one main scale division (M.S.D.) and one vernier scale division (V.S.D.) as it is the smallest distance that can be measured using the instrument.

n V.S.D. = (n – 1) M.S.D.

Formulas Used:

(a) Least count of vernier callipers =  the magnitude of the smallest division on the main scale (÷) the total number of small divisions on the vernier scale 

(b) Density of a rectangular body = mass (÷) volume = m (÷) V l.b.h, where m is its mass, l its length, b its breadth and h the height. 

(c) The volume of a cylindrical (hollow) object V = πr2h' = π D′2 (÷) 4 * h where h' is its internal depth, D' is its internal diameter and r is its internal radius.

PROCEDURE: 

(a) Determining the diameter of a small cylindrical or spherical object.

1. Maintain the Vernier Callipers' closed jaws. Keep an eye on the main scale's zero point. It must have exact alignment with the vernier scale. If the opposite is true, take into consideration the zero error for each observation that will be made while using the instrument.

2. Find a division on the vernier scale that corresponds to a division on the main scale. If a magnifying glass is available, use it to count the divisions on the Vernier scale that match the ones on the primary scale. Aim to place your eye directly over the dividing mark to prevent parallax errors.

3. To release the movable jaw, gently unscrew the screw. Slide it just enough to hold the sphere/cylindrical body gently (but not too tightly) in between the lower jaws AB. The jaws should be precisely perpendicular to the body's diameter. Gently tighten the screw to secure the instrument to the body in this position.

4. Take careful note of where the vernier scale's zero mark is in relation to the larger scale. It usually won't line up exactly with any of the minor divisions on the primary scale. Just to the left of the vernier scale's zero point, note the primary scale division.

5. From the left end (zero) to the right of the vernier window, start looking for an identical match between a vernier scale division and a main scale division. Note its number, let's say N, with care.

6. To the major scale reading indicated in step 4, multiply "N" by the instrument's lowest count and then add the result. For addition to be valid, make sure the product is transformed into the correct units (often cm).

7. Repetition of steps 3-6 will allow you to measure the diameter of the body at various points along its curved surface. In each scenario, read three times.

8. Observations should be recorded in tabular form with the appropriate units. If necessary, make a zero correction.

9. Calculate the arithmetic mean of the body's diameter readings after they have been rectified. Include the right amount of significant figures and appropriate units when expressing the results.

(b) Measuring a regular rectangular body's dimensions to ascertain its density.

1. Using an appropriate ruler, measure the length of the rectangular block if it extends past the reach of the Vernier callipers' expanded jaws. If not, after holding the block lengthwise between the Vernier Callipers' jaws, repeat steps 3-6 as shown in (a).

2. Holding the rectangular block in the appropriate positions, repeat steps 3-6 described in (a) to obtain the other measurements (breadth b and height h).

3. Using the correct units and statistically significant values, tabulate the observations for the rectangular block's length, width, and height. Anywhere zero corrections are required, apply them.

4. Calculate the arithmetic mean of the measurements taken independently for height, width, and length.

(c) Measuring the beaker's (or other cylindrical object) internal diameter and depth to determine its internal volume.

1. Set the Vernier Callipers' upper jaws CD so that they touch the beaker's wall from the inside without applying excessive pressure. To maintain the Vernier Callipers in this position, lightly tighten the screw.

2. To determine the beaker/calorimeter's interior diameter, repeat steps 3-6 as in (a). Do this for the beaker in two separate (angular) positions.

3. Maintain the main scale of the Vernier Callipers' main scale on its periphery to measure the beaker's depth. This should be done in a way that allows the strip's tip to freely move down the depth of the beaker.

4. Continue sliding the Vernier Callipers' movable jaw up and down until the strip just touches the beaker's bottom. Make sure it does so with the bottom surface completely perpendicular. Now tighten the Vernier Callipers' screw.

5. Repeat steps 4 through 6 from portion (a) of the experiment to determine the beaker's depth. Get depth readings from the breaker's various places.

6. Using the appropriate units and statistically significant figures, tabulate the observations. If necessary, make no adjustments at all.

7. Calculate the mean of the corrected measurements for the specified beaker's internal diameter and depth. Put the result in the appropriate units and significant figures.

OBSERVATIONS:

(i) Least count of Vernier Callipers (Vernier Constant) 

1 main scale division (MSD) = 1 mm = 0.1 cmNumber of vernier scale divisions, N = 1010 vernier scale divisions = 9 main scale divisions1 vernier scale division = 0.9 main scale divisionVernier constant = 1 main scale division – 1 vernier scale division                           = (1– 0.9) main scale divisions                           = 0.1 main scale division

Vernier constant (VC ) = 0.1 mm = 0.01 cm

Alternatively,Vernier constant (VC ) = 0.1 mm = 0.01 cm

(ii) The zero error and how to fix it

The zero of the Vernier should match the zero of the primary scale when jaws A and B come into contact. If not, the measurement device is said to have zero error (e). Depending on whether the zero of the vernier scale is to the right or left of the zero of the main scale, the zero error may be positive or negative. The observed readings in this instance need to be corrected.

(iii) Positive zero error

It provides an illustration of this type of error. One can see from the figure that while both jaws are touching, the vernier scale's zero is displaced to the right of the main scale's zero (this could have happened as a result of a manufacturing flaw or hard handling). Given this circumstance, it is evident that the reading obtained during measurement will be higher than the actual value. As a result, a correction that is proportional to the right shift of the vernier scale's zero must be used.Zero on the vernier scale should ideally match zero on the main scale, The fifth vernier division and the main scale reading coincide.

∴ Least Count = + 0.05 cm; Zero Error = + 5

∴ Zero Error = + 5 × Least Count = + 0.05 cm

Hence, the zero error is positive in this case. For any measurements done, the zero error (+ 0.05 cm in this example) should be ‘subtracted’ from the observed reading.

∴ True Reading = Observed reading – (+ Zero error)

(iv) A negative zero error

It provides a negative zero error illustration. This image demonstrates how the zero of the vernier scale is moved to the left of the zero of the main scale when the jaws are touching. This circumstance clearly shows that when taking measures, the reading obtained will be lower than the reading obtained. As a result, a correction that is inversely inversely proportionate to the leftward displacement of the vernier scale's zero must be made.

5th vernier scale division is coinciding with a main scale reading. 

∴ Zero Error = – 5 × Least Count = – 0.05 cmNote that the zero error in this case is considered to be negative. For any measurements done, the negative zero error, ( –0.05 cm in this example) is also substracted ‘from the observed reading’, though it gets added to the observed value.

∴ True Reading = Observed Reading – (– Zero error)

(i) Zero error  no zero error    (ii) positive zero error   (iii) negative zero error

PRECAUTIONS:

1. Use machine oil or lubricant to make the vernier scale slide over the main scale more easily.

2. Screw the vernier firmly but without applying excessive pressure to prevent harm to the screw's threads.

3. To prevent parallax errors, keep your gaze directly over the dividing mark.

4. Record each observation with the appropriate units and significant figures.

SOURCES OF THE ERROR:

Using Vernier Callipers, any measurement is likely to be inaccurate if

(i) the instrument's zero error is not taken into account; 

(ii) The Vernier Callipers are not properly positioned in relation to the body, which includes preventing gaps and excessive pressure, if not both.

RESULTS:

(a) Diameter of the spherical/ cylindrical body, D = ...× 0.01m 

(b) Density of the given rectangular block, ρ = ... kg /m³(c) Internal volume of the given beaker V'= ... m³