2 MEASUREMENT OF LENGTH, AND
DIAMETER BY VERNIER CALIPER, AND
MICROMETER
If there’s one thing all scientists do a lot of, it’s measure. Science is a quantification process, and from
this quantification comes insight into the nature of the universe. Every week you will be measuring in
lab, and you will draw from these measurements a conclusion. But in order to measure you must first
be proficient with the tools of the trade: the Vernier caliper, the micrometer, the meterstick, etc.
2.1 Goal:
1 To become familiar with several of the mechanical measuring devices used in physics
2 To determine the length, height and diameter of the given work piece using vernier caliper, and
micrometer.
2.2 Measuring Devices:
Here are a few top tips when you use your micrometer screw gauge and your vernier callipers:
i Remember to take your zero error readings, ideally both before and after your main experiment.
ii Take at least three readings of the object in different places on the object, for example at different
positions along a piece of wire, and then take an average for later calculations - the object may
not be completely uniform.
iii If the object is spherical or cylindrical (such as a ball bearing or a wire) then remember to take
the readings at different orientations as well as at different places, as the object may have become
deformed in one particular orientation.
The Vernier Calliper:
Procedure: How to use Vernier Calipers
1 Unlock the lock screw and press the thumb screw down. Open the jaws.
2 Close the jaws around the object you want to measure or, for inside measurements open them un-
til the fill the gap you wish to measure, or insert the depth rod into the hole you wish to measure.
2.2 Measuring Devices:
3 Tighten the lock screw so that the jaws do not move.
4 Now read the scale.
Formula used for reading Vernier Calipers:
Formula used
Dimensions measured =Main scale reading + Vernier scale reading × vernier constant
L = ℓ + [p × (v.c.)] v.c. = 0.1 mm = 0.01 cm
L is the length of the object, ℓ is the reading of the main scale, and p is the vernier
scale reading, v.c. is vernier constant.
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2.2 Measuring Devices:
Zero error and its correction:
Figure 2.1: Zero error (i) no zero error (ii) positive zero error (iii) negative zero error.
Positive zero error:
Zero Error, e = (+z) × v.c. = (+5 × 0.01) cm = +0.05 cm as in Fig. 2.1
Negative zero error:
Zero Error, e = (+z – 10) × v.c. = (5 – 10) × 0.01 cm = –0.05 cm as in Fig. 2.1
The true reading:
True Reading = Observed Reading – (±e)
Example 2.1 Correcting for zero errors with manual vernier callipers
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2.2 Measuring Devices:
Exercise 2.1
What is the vernier capiller reading?
Main scale reading (MSR) = mm
Vernier scale reading (VSR) =( × ) mm = mm
The final reading (MSR + VSR) = mm + mm = mm
= cm
Exercise 2.2
What is the vernier capiller reading?
Main scale reading (MSR) = mm
Vernier scale reading (VSR) =( × ) mm = mm
The final reading (MSR + VSR) = mm + mm = mm
= cm
Experimental Measurements: Mesurments of hollow cylinder
(i) (ii) (iii) Average value (cm)
Outer diameter d (cm)
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2.2 Measuring Devices:
(i) (ii) (iii) Average value (cm)
Inner diameter d (cm)
(i) (ii) (iii) Average depth (cm)
Depth l (cm)
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2.2 Measuring Devices:
The Micrometer Or The Micrometer screw gauge:
How to use a Micrometer Screw Gauge
1 Open the micrometer by turning the thimble or ratchet.
2 Place the object to be measured between the spindle and anvil.
3 Close the spindle by turning the ratchet, not the thimble. The ratchet prevents excess pressure
on the object being measured, so you don’t squash it and get a false reading.
4 Now read the scale.
Formula used for reading micrometer:
Formula used
Dimensions measured =Main scale reading + (Thimble scale reading × Least count)
L =ℓ + [s × (L.C.)]
Where L is the reading of an object between the studs, ℓ represents the linear scale
reading, and s represents the number of circular scale divisions, sth division coincid-
ing with the reference line.
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2.2 Measuring Devices:
Zero errors
Zero errors can be either positive or negative.
Correcting for zero errors with a micrometer Table. 2.2 explains how to how to take account of
zero errors for manually read micrometer screw gauges.
Exercise 2.3
Read the zero errors shown below:
Zero error = ( ) mm Zero error = ( ) mm Zero error = ( ) mm
This zero error should be subtracted from the observed reading.
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2.2 Measuring Devices:
Exercise 2.4
What is the Micrometer reading?
Main scale reading (MSR) = ( ) mm | Main scale reading (MSR) = ( ) mm
Thimble scale reading (TSR) = ( ) mm | Thimble scale reading (TSR) = ( ) mm
Measured length = MSR + TSR | Measured length = MSR + TSR
=( )+( ) mm | =( )+( ) mm
=( ) mm | =( ) mm
Experimental Measurements:
Measurments of rod diameter:
(i) (ii) (iii) Average Diameter
Diameter d (mm)
(mm)
Measurments of slice thickness:
(i) (ii) (iii) Average thickness
Thickness t (mm)
(mm)
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