Use of Vernier Callipers to
Vernier Callipers, Spherical body, such as a pendulum bob or a glass marble, rectangular block of known mass and cylindrical object like a beaker/glass/calorimeter
1. A Vernier Calliper has two scales-one main scale and a Vernier scale, which slides along the main scale. The main scale and Vernier scale are divided into small divisions though of different magnitudes.
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 and metallic strip are designed to measure the distance/ diameter of objects. 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.
2. The least count of a common scale is 1mm. It is difficult to further subdivide it to improve the least count of the scale. A vernier scale enables this to be achieved.
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.
Formulas Used
n V.S.D. = (η-1) M.S.D.
Measuring the diameter of a small spherical or cylindrical body.
Measuring the dimensions of a regular rectangular body to determine its density.
Measuring the internal diameter and depth of the given beaker (or similar cylindrical object) to find its internal volume.
Least count of Vernier Callipers (Vernier Constant)
1 main scale division (MSD) = 1 mm = 0.1 cm
Number of vernier scale divisions, N = 10
10 vernier scale divisions = 9 main scale divisions
1 vernier scale division = 0.9 main scale division
Vernier constant = 1 main scale division -1 vernier scale division
= (1-0.9) main scale divisions
= 0.1 main scale division
Vernier constant (V_{c}) = 0.1 mm = 0.01 cm
Alternatively,
Vernier constant = 1MSD/N = 1MM/10
Vernier constant (V _{c}) = 0.1 mm = 0.01 cm
Zero error and its correction
When the jaws A and B touch each other, the zero of the Vernier should coincide with the zero of the main scale. If it is not so, the instrument is said to possess zero error (e). Zero error may be
When the jaws A and B touch each other, the zero of the Vernier should coincide with the zero of the main scale. If it is not so, the instrument is said to possess zero error (e). Zero error may be
Positive zero error
Fig E 1.2 (ii) shows an example of positive zero error. From the figure, one can see that when both jaws are touching each other, zero of the vernier scale is shifted to the right of zero of the main scale (This might have happened due to manufacturing defect or due to rough handling). This situation makes it obvious that while taking measurements, the reading taken will be more than the actual reading. Hence, a correction needs to be applied which is proportional to the right shift of zero of vernier scale.
In ideal case, zero of vernier scale should coincide with zero of main scale. But in Fig. E 1.2 (ii), 5th vernier division is coinciding with a main scale reading.
∴ Zero Error = + 5 x 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)
Negative zero error
Fig. E 1.2 (iii) shows an example of negative zero error. From this figure, one can see that when both the jaws are touching each other, zero of the vernier scale is shifted to the left of zero of the main scale. This situation makes it obvious that while taking measurements, the reading taken will be less than the actual reading. Hence, a correction needs to be applied which is proportional to the left shift of zero of vernier scale.
In Fig. E 1.2 (iii), 5th vernier scale division is coinciding with a main scale reading.
∴ Zero Error = - 5 x Least Count
Note 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)
Table E 1.1 (a): Measuring the diameter of a small spherical/ cylindrical body
S. No. | Main Scale reading, M (cm/mm) | Number of coinciding vernier division, N | Vernier scale reading, V = N x V _{c} (cm/mm) | Measured diameter, M + V (cm/mm) |
1 | ||||
2 | ||||
3 | ||||
4 |
Zero error, e = ± ... cm
Mean observed diameter = ... cm
Corrected diameter = Mean observed diameter - Zero Error
Table E 1.1 (b) : Measuring dimensions of a given regular body (rectangular block)
Dimension | S. No. | Main Scale reading, M (cm/mm) | Number of coinciding vernier division, N | Vernier scale reading, V = N x V _{c} (cm/mm) | Measured diameter, M + V (cm/mm) |
Length ι 1/2/3 | |||||
Breadth (b) 1/2/3 | |||||
Height (h) 1/2/3 |
Zero error = ± ... mm/cm
Mean observed length = ... cm, Mean observed breadth = ... cm
Mean observed height = ... cm
Corrected length = ... cm; Corrected breath = ... cm;
Corrected height = ...cm
Table E 1.1 (c) : Measuring internal diameter and depth of a given beaker/ calorimeter/ cylindrical glass
Dimension | S. No. | Main Scale reading, M (cm/mm) | Number of coinciding vernier division, N | Vernier scale reading, V = N x V _{c} (cm/mm) | Measured diameter, M + V (cm/mm) |
Internal diameter (D') 1/2/3 | |||||
Depth (h') 1/2/3 |
Mean diameter = ... cm
Mean depth= ... cm
Corrected diameter = ... cm
Corrected depth = ... cm
Measurement of diameter of the sphere/ cylindrical body
Mean measured diameter, D_{0}= D_{1} + D_{2} +....+D_{6}/6 cm
Do = ... cm = ... x 10 ^{-2} m
Corrected diameter of the given body, D = Do -( ± e ) = ... x 10 ^{-2} m
Measurement of length, breadth and height of the rectangular block
Mean measured length, ι _{0} = ι _{1} + ι _{2} + ι _{3}/3 cm
ι _{0} = .....cm = ..........x 10 ^{-2} m
Mean observed breadth, b_{0} = b_{1} + b_{2} + b_{3}/3
Mean measured breadth of the block, b_{0} = ... cm = ... x 10 ^{-2} m
Corrected breadth of the block,
Mean measured breadth of the block, b = b_{0} -(±e) cm = ... x 10 ^{-2} m
Mean measured height of block, h_{0} = h_{1} + h_{2} + h_{3}/3
Corrected height of block h = h_{0}-( ± e ) = ... cm
Volume of the rectangular block,
V = ιbh = ... cm ^{3} = ... x 10 ^{-6} m ^{3}
Density ρ of the block
ρ = m/V = ......kgm ^{-3}
Measurement of internal diameter of the beaker/glass
Mean measured internal diameter,D_{0} = D _{1} + D _{2} + D _{3}/3 cm
D _{0} = .....cm = ..........x 10 ^{-2} m
Corrected internal diameter,
D = D_{0} -(±e) cm = ... x 10 ^{-2} m
Mean measured depth of the beaker, h_{0} = h_{1} + h_{2} + h_{3}/3
= ... cm = .......x 10 ^{-2} m
Volume of the rectangular block,
Corrected measured depth of the beaker
h = h_{0} -(±e) cm = ... x 10 ^{-2} m
Internal volume of the beaker
V = π D ^{2}h/4 = ......x 10 ^{-6}m _{3}
(a) Diameter of the spherical/ cylindrical body,
D = .....x 10 ^{-2}m
(b) Density of the given rectangular block,
ρ = ........kgm ^{-3}
(c) Internal volume of the given beaker
V' = .....m ^{-3}
Any measurement made using Vernier Callipers is likely to be incorrect if
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