Aim:
To measure (a) diameter of a small spherical/cylindrical body and (b) to measure internal diameter and depth of a given beaker/calorimeter using Vernier Callipers and (c) hence find its volume

Apparatus:

1. Vernier Calliper
2. Cylinder (Metal)
3. Beaker Graduated

Theory:

A Vernier Calliper has two scales–one main scale and a Vernier scale. Vernier Scale slides along the main scale. The main scale and Vernier scale are divided into small divisions though of different magnitudes. Generally, each division of Vernier scale is smaller than each division of main scale. In our example nine main scale division is equals to ten vernier divisions.

The main scale is graduated in cm and mm. It has two fixed jaws, A and C, projected at right angles to the scale. The sliding Vernier scale has jaws (B, D) projecting at right angles to it and also the main scale and a metallic strip (N). The zero of main scale and Vernier scale coincide when the jaws are made to touch each other. The jaws (A, B) are used to measure external diameter of an object, Jaws (C, D) are used to measure internal diameter of an object and metallic strip are designed to measure the height / depth of any object. Knob P is used to slide the Vernier scale on the main scale. Screw S is used to fix the Vernier scale at a desired position. The least count of a common scale is 0.1 cm or 1 mm. It is difficult to further subdivide it to improve the least count of the scale. A Vernier scale enables this to be achieved.

Fig. 1.1

Principle:

Determination of Least Count or Vernier Constant:

The difference in the magnitude of one main scale division (M.S.D.) and one Vernier scale division (V.S.D.) is called the least count of the instrument, as it is the smallest distance that can be measured using the instrument.  For an instrument where Vernier is used its Vernier Constant (VC) is its  Least Count (LC).

From fig 1.1, 10 division of Vernier scale coincides with 9 division of main scale and the length of 1 division on main scale is 1 mm.

                                10 Vernier Scale Division (VSD) = 9 Main Scale Division (MSD)

                                1 VSD =  MSD

The quantity (1 MSD – 1 VSD) is called Vernier Constant (VC).

                                VC = (1 - ) MSD  = MSD =

                                                =   × 1 mm       (1 MSD = 1mm)

                                VC = 0.1mm = 0.01cm

The volume of the spherical object is:

V = , Where r is the radius of the sphere.  

Determination of Zero Error:

If the zero of main scale coincides with zero of Vernier scale when jaws C and D are brought in contact with each other, then the instrument is free from error as shown in fig. 1.2. But in actual practice it is never so. Due to wear and tear of jaws and sometimes due to manufacturing defects the zero mark of the Vernier scale does not coincide with zero of main scale. It gives rise to an error called zero error. Zero error can be positive or negative.

Fig. 1.2

(i) Positive zero error and its correction:   

The zero error is positive when the zero mark of the Vernier scale shifted towards the right side of the zero of main scale when jaws C and D are made to touch each other. In such case, measured length will be more than the actual length and, therefore, the zero error is called positive zero error. Hence, we have to subtract positive error from the actual error.  If, for example,  the 3rd Vernier mark coincides with any main scale reading as shown in the fig 1.3,  then the Zero error is:

Zero error           = 0.00 + 3 x Least Count = 0.00 + 3 x 0.01

Zero error           = 0.03 cm 

Hence, the Actual reading  =  Measured reading – (0.03)

Fig. 1.3

(ii) Negative zero error and its correction:

The zero error is negative when the zero mark of the Vernier scale shifted towards the left side of the zero of main scale when jaws C and D are made to touch each other. In such case, measured length will be less than the actual length and, therefore, the zero error is called negative zero error. Hence, we have to add negative error with the actual error If, for example,  the 8th Vernier mark coincides with a main scale reading as shown in the fig 1.4,  then the Zero error is:

Zero error           = 0.00 - (10-8)** x Least Count = 0.00 - 2 x 0.01

Zero error           =  -0.02 cm

Hence, the Actual reading  =  Measured reading – (-0.03)

Fig. 1.4

** to calculate negative error we count the coincide mark from the opposite side which is from 10 to 0 of the Vernier scale.

Fig. 1.5

Fig. 1.6

Fig. 1.7

Procedure:

1. Determine the Vernier constant (V.C.) i.e., least count of the Vernier callipers as explained above and record it.
2. Bring the movable jaw BD in close contact with the fixed jaw AC and find the zero error. Do it three times and record it. If there is no zero error, then record, zero error nil. If it does not coincide, then find the zero error and record it.

Measurement of diameter of spherical body

1. With the help of lower jaws (A,B) grip the spherical body gently without undue pressure. As shown in fig.1.5.  Tight the screw S attached to the Vernier scale.
2. Record the main scale reading (N) just before the zero mark of the Vernier scale in Table 1.1.
3. Note the number (n) of the Vernier scale division which coincides with some division of the main scale.
4. Repeat steps 4 and 5 after rotating the body by 90° for measuring the diameter in a perpendicular direction.
5. Take at least four observations along different directions and apply zero correction.
6. Take the mean of all recorded diameters.

Measurement of internal diameter

1. Put the jaws C and D inside the beaker or calorimeter and open them till each of them touches the inner wall of the beaker or calorimeter, without any undue pressure on the walls as shown in fig. 1.6. Tight the screw S attached to the Vernier scale gently.
2. Note the-position of the zero mark of the Vernier scale on the main scale. Record the main scale reading just before the zero mark of the Vernier scale in Table 1.2. This reading is called main scale reading (M.S.R.).
3. Note the number (n) of the Vernier scale division which coincides with some division of the main scale.
4. Repeat steps 10 and 11 after rotating the Vernier callipers by 90° for measuring internal diameter in a perpendicular direction.
5. Find total reading and apply zero correction.

Measurement of depth.

1. Keep the edge of the main scale of Vernier calliper on its peripheral edge. This should be done in such a way that the tip of the strip is able to go freely inside the beaker along its depth as shown in fig. 1.7.
2. Keep sliding the moving jaw of the Vernier callipers until the strip just touches the bottom of the beaker. Take care that it is just perpendicular to the bottom surface. Now tighten the screw S of the Vernier callipers.
3. Repeat steps 14 and 15 for four different positions along the circumference of the upper edge of the beaker or calorimeter.
4. Find total reading and apply zero correction in Table 1.3.
5. Take mean of two different values of internal diameter and four different values of the depth.
6. Calculate the volume by using proper formula and show that in the result with proper unit.

Observations:

Determination of Vernier constant :

1 smaller div. of the main scale (MSD) = ______mm or ______cm

_____ Vernier  division (VSD) = _____MSD

1 VSD = ______ MSD = ______ mm or ______cm

So, VC = 1 MSD -1 VSD = _______ mm or _______cm

Zero error, e = ± _______mm or _______cm

Table 1.1 Measuring the diameter of spherical body

[(a) and (b) corresponds to mutually perpendicular diameters.]

Mean corrected diameter, Ds: __________________(cm/mm)

Table 1.2 Determination of internal diameter of a Beaker/Calorimeter

[(a) and (b) corresponds to mutually perpendicular diameters.]

Mean corrected diameter of beaker, DB: _________________(cm/mm)

Table 1.2 Determination of depth a Beaker/Calorimeter

[(a) and (b) corresponds to mutually perpendicular diameters.]

Mean corrected depth, h: __________________(cm/mm)

Calculation:

Diameter of the sphere, Ds = ………………………………cm

Radius of the sphere, rs =  = _____________cm

Internal diameter of beaker, DB = ………………………..cm

Radius of beaker, rb =   = ________cm

Depth of beaker, h =…………………………………… cm

Volume of beaker or calorimeter, VB =  cm3 = ………………………………….cm3

Volume of spherical object, Vs =  cm3= ………………………………..cm3

Precautions :

1. If the motion of the Vernier scale over the main scale is not smooth, a little oiling may be needed.
2. The experimental body should be held firmly but gently between the two jaws of callipers. Excess pressure may damage the body.
3. If the diameters measured at right angles to each other at a place are found to differ much, both the values should be rejected as the body is obviously not uniform at that plane.
4. When taking the readings, the line of sight should be normal to scale where reading is taken, to avoid the parallax error.

Sources of error:

1. The Vernier scale may be loose on the main scale.
2. The jaws may not be at right angle to the main scale.
3. Parallax may be there while taking readings.
4. Zero error in the depth measurement may be different and it should be determined separately. In fact when the two jaws touch each other, the strip, in perfect condition, should be in line with the edge of the main scale. But after repeated use it is found to go a little inside and there is zero error. In this case the strip and the edge of the scale are brought in line will each other and the corresponding reading of the Vernier scale is taken. This is the zero error and it should be subtracted from the reading.

Reference:

1. http://www.ncert.nic.in/
2. https://www.learncbse.in/

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