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1. Measurements
and
Measuring Instruments

2. Measurement

3. Measurement
Physics can also be defined as the branch of
science dealing with the study of properties of
materials. To understand the properties of
materials, measurement of physical quantities
such as length, mass, time etc., are involved. The
uniqueness of physics lies in the measurement of
these physical quantities.

4. Fundamental quantities and derived
quantities
Physical quantities can be classified into two
namely, fundamental quantities and derived quantities.
Fundamental quantities are quantities which cannot be
expressed in terms of any other physical quantity.
For example, quantities like length, mass, time,
temperature are fundamental quantities. Quantities that
can be expressed in terms of fundamental quantities are
called derived quantities. Area, volume, density etc. are
examples for derived quantities

5. Unit
To measure a quantity, we always compare it with
some reference standard. To say that a rope is 10 metres
long is to say that it is 10 times as long as an object
whose length is defined as 1 metre. Such a standard is
called a unit of the quantity.
Therefore, unit of a physical quantity is defined as
the established standard used for comparison of the given
physical quantity.
The units in which the fundamental quantities are
measured are called fundamental units and the units used
to measure derived quantities are called derived units.

6. Physical quantity Unit Symbol
Fundamental quantities
Length
Mass
Time
Electric current
Temperature
Luminous intensity
Amount of substance
metre
kilogram
second
ampere
kelvin
candela
mole
m
kg
s
A
K
cd
mol
Supplementary quantities
Plane angle
Solid angle
radian
steradian
rad
sr

7. SI standards

8. Length

9. Length
Length is defined as the distance
between two points. The SI unit of length is metre.
One standard metre is equal to 1 650763.73
wavelengths of the orange − red light emitted by the
individual atoms of krypton − 86 in a krypton
discharge lamp.

10. Mass

11. Mass
Mass is the quantity of matter contained in a body. It
is independent of temperature and pressure. It does not vary
from place to place. The SI unit of mass is kilogram

12. Time

13. Time
Until 1960 the standard of time was based on the
mean solar day; In 1967, an atomic standard was
adopted for second, the SI unit of time.
One standard second is defined as the time taken
for 9 192 631 770 periods of the radiation
corresponding to unperturbed transition between
hyperfine levels of the ground state of cesium − 133
atom. Atomic clocks are based on this. In atomic
clocks, an error of one second occurs only in 5000
years.

14. ELECTRIC CURRENT

15. Ampere
The ampere is the constant current which,
flowing through two straight parallel infinitely long
conductors of negligible cross-section, and placed
in vacuum 1 m apart, would produce between the
conductors a force of 2X10-7 newton per unit
length of the conductors.

16. Temperature

17. Kelvin
It is the primary unit of temperature.
The Kelvin is the fraction of 1 / 273.16 of
the thermodynamic temperature of the triple point
of water*.

18. Temperature
Freezing point of water is 0° C in celcius scale
but at 0° C, water molecules do not come to rest.
-273° C molecules come to rest.
-273° C is absolute zero and it is taken as null point
for Kelvin scale.
-273° C = 0 k
273 k = 0° C
The usage of negative values in celcius scale can be
avoided by using Kelvin scale.

19. Luminous
Intensity

20. Candela
The candela is the luminous intensity in a
given direction due to a source, which emits
monochromatic radiation of frequency 540×1012
Hz and of which the radiant intensity in that
direction is 1 / 683 watt per steradian

21. AMOUNT OF
SUBSTANCE

22. Mole
The mole is the amount of substance which
contains as many elementary entities as there are
atoms in 0.012 kg of carbon-12.

23. Rules and conventions
for writing SI units and
their symbols

24. 1. The units named after scientists are not written
with a capital initial letter.
For example : newton, henry, watt

25. 2. The symbols of the units named after scientist
should be written by a capital letter.
For example : N for newton, H for henry, W
for watt

26. 3. Small letters are used as symbols for units not
derived from a proper name.
For example : m for metre, kg for kilogram

27. 4. No full stop or other punctuation marks
should be used within or at the end of symbols.
For example : 50 m and not as 50 m.

28. 5. The symbols of the units do not take plural
form.
For example : 10 kg not as 10 kgs

29. 6. When temperature is expressed in kelvin, the
degree sign is omitted.
For example : 273 K not as 273° k
(If expressed in Celsius scale, degree sign is to be
included. For example 100° C and not 100 C)

30. 7. Use of solidus is recommended only for
indicating a division of one letter unit symbol by
another unit symbol. Not more than one solidus is
used.
For example : m s−1 or m / s, J / K mol or
J K-1 mol-1 but not J / K / mol.

31. 8. Some space is always to be left between the
number and the symbol of the unit and also
between the symbols for compound units such as
force, momentum, etc.
For example, it is not correct to write 2.3m.
The correct representation is 2.3 m;
kg m s–2 and not as kgms-2

32. 9. Only accepted symbols should be used.
For example : ampere is represented as A
and not as amp. or am ; second is represented as
s and not as sec.

33. 10. Numerical value of any physical quantity
should be expressed in scientific notation.
For an example, density of mercury is
1.36 × 104 kg m−3 and not as 13600 kg m−3.

34. S.No PSR
(mm)
HSC
(div)
HSR=HSC
XLC
CHSR
=
HSR+_
ZC
TR=
PSR+
CHSR
To Find the thickness “d” of the bar using screw
gauge
L.C=0.01 mm Z.E= Z.C=

35. To Find the breadth of the bar ‘b’ using vernier
caliper : L.C=0.01 cm
S.No MSR
(cm)
VSC VSR =
VSCX LC
(cm)
TR= MSR +
VSR
(cm)

36. Importance Of Accurate Measurements
Human beings are able to make more
accurate measurements. A lot therefore depends on
the instruments that are used to make the
measurements.

37. THREE CHARACTERISTICS OF
MEASURING INSTRUMENTS
There are three important characteristics of
measuring instruments that one must be
familiar with. They are:
ƒƒ
Least Count
ƒƒ Range
ƒƒ Zero Error

38. ƒƒLeast Count
The smallest value that any instrument can
measure is called the least count of the instrument.
For example, if you use a scale then the
smallest division is one millimeter. It is the smallest
value that the scale can measure and is called the least
count of the scale.

40. Range
The values between the minimum measurable
value and the maximum value that can be measured
is called the range of the instrument. For example,
the range of the scale is zero centimeter to thirty
centimeters. Usually, we state the maximum value as
the range since the minimum value is generally zero.
When we say, the range of the metre scale is 100cm,
we mean that the range is from zero to 100cm.

41. There are, however, special instruments that are
designed to measure from a specific minimum
value to a maximum value. In such cases we say
the range of the instrument is from such and such
value to such and such value.
For example, if you had a Voltmeter that
reads from 150V to 250V, then we say that the
range of the Voltmeter is from 150V to 250V.
Usually such instruments are built for a specific
purpose and optimized to give accurate readings
within the design range and the designer expects
that the value will not go outside the design range.

42. Zero Error
Often instruments do not read zero at the
minimum position. For example, the needle of an
Ammeter may read 0.02 amperes when it is not
connected to the circuit. Such an error is called zero
error, since the needle at the minimum position is not
reading zero. While using the instrument, one has to
apply a correction to the reading to obtain the real
value. The value that is read off the instrument is called
the observed value to which we apply the zero error
correction and obtain the measured value.

43. MEASURING LENGTH
Vernier caliper
The vernier caliper is a device that is used a
great deal in engineering work and in workshops
which manufacture things. It is an ingenious device
where two scales with fairly large least counts are used
in conjunction with one another to measure very small
values of length.
The auxiliary scale, now called the Vernier scale
after the inventor, is used nowadays in almostn every
instrument meant for accurate measurement such as the
barometer, the microscope, etc.

44. The principle of the vernier
The principle of the Vernier is delightfully simple. Let us say, you have
two scales, one with a least count of 1.0mm(main scale) and the other with a least
count of 0.9mm (auxiliary or Vernier scale) you can then measure an object
whose length is 0.1mm quite easily. Refer to the diagram alongside; by aligning
the left edge of the object with the zero of the main scale and butting the edge of
the auxiliary scale to the edge of the object, you would find that the first marking
of the auxiliary scale would exactly coincide with the first marking of the main
scale (object length, 0.1mm + vernier division, 0.9mm = 1.0mm, the first main
scale division). Going the other way around, if we did not know the size of the
object and we found that the first vernier division coincided with the first main
scale division, we could state that the size of the object must be 0.1mm, since:-
object length, 0.1mm = 1.0mm, the first main scale division - vernier division,
0.9mm You could now say that the least count of the combination of scales is 0.1
mm, which is the difference between the two least counts.

45. Popularly it is written as follows:-
L.C. (of the instrument) = 1 MSD – 1 VSD
If on the other hand, the size of the object being measured is 0.2mm long and
the auxiliary scale is butted against the object the second vernier marking will coincide
with the second main scale division (object length, 0.2mm + two vernier divisions, 1.8mm
= 2.0mm).
Going the other way around, if we did not know the size of the object and we
observed that the second vernier division coincided with the second main scale division
we could say that the size of the object is 0.2mm. object length, 0.2mm = 2.0mm, the
second main scale division – two x vernier divisions, 1.8mm
There is a pattern here and we could try extending by using the same logic and saying that
if the object was 0.4mm long then the fourth vernier division would coincide with the
fourth main scale division.Further if it was 0.9mm long, then the ninth vernier division
would coincide with the ninth main scale division. I could write this
as:
Object length, 0.9mm = 9.0mm,
The ninth main scale division – nine x vernier divisions, 8.1mm
0.9mm = 9 * Main scale division – 9 * Vernier scale division

46. Description of vernier caliper
The Vernier Caliper used in the laboratory is a modern version of the
age-old one. A picture of a Vernier Caliper is shown below.
The Vernier Caliper consists of :-
ƒƒA thin long steel bar graduated in cm and mm (4). This is the Main scale.
ƒƒFixed perpendicular to the bar at the left end of the steel bar carrying the main scale
is an upper fixed jaw and a lower fixed jaw.
ƒƒTo the right of the fixed jaws mounted on the steel bar is a slider with a upper movable
jaw and a lower movable jaw.
ƒƒThe slider can be fixed to any position using the tightening screw or friction nut.
ƒƒThe Vernier scale (6) is marked on the slider and moves along with the movable
jaws and the slider.
ƒƒThe lower jaws (1) are used to measure the external dimensions and the upper jaws
(2) are used to measure the internal dimensions of objects.
ƒƒThe thin bar attached to the Vernier scale at the right side (3) is called the depth probe
and is used to measure the depth of hollow objects.

47. Using the vernier caliper
The first step in using the vernier Caliper is to
find out its characteristics Least count, Range and
Zero error.

48. 1. Lower Jaws
1a. Lower Fixed Jaw
1b. Lower Movable Jaw
2. Upper Jaws
2a. Upper Fixed Jaw
2b. Upper Movable Jaw
3. Depth Probe
4. Main Scale
5. Retainer
6. Vernier
7. Friction Nut
8.Slider
1. Least Count:
2. Zero Error
3. Positive zero error
4. Negative zero error

49. Positive zero error

50. Negative zero error

51. 5.5.5. Digital vernier caliper
Digital Vernier Caliper has a digital display on the slider. The slider also houses the
electronic calculator which calculates the measured value that is then displayed. The
user need not manually calculate the least count, the zero error etc. or take the trouble
of finding the vernier coincident manually.

52. 5.6. MEASURING MASS
When we go to a shop to buy something, say a kg of rice, we often buy it in terms of
the
‘weight’. In layman’s parlance what is called ‘weight’ is actually mass in science
parlance.
Many things are measured in terms of the mass in the commercial world. We buy
gold
which is measured in grams or milligrams, medicines in 500mg or 250mg values,
load
trucks in terms of tons etc.

53. Common (beam) balance
A beam balance compares the sample
mass with a standard reference mass
(known masses such as 100g, 200g etc.).
Least counts of 20g to 50 mg are possible.

54. Two pan balance
This type of balance is commonly used for measuring mass in shops. This
balance too compares the sample mass with a standard reference mass. The pans rest on
top of the beam and can be conveniently placed on a table top. Least counts are
generally in the region of 10g to 50g.

55. Physical balance
It is used in laboratories. It is similar to the beam balance but is a lot more
sensitive and can measure mass of an object correct to a milligram.

56. 5.7. MEASURING TIME
The pendulum as a reliable measure of time was first articulated by Galileo
in 1602. In those days many lamps would be mounted on a large glass arrangement
suspended from the ceiling. Such an elaborate arrangement was called a
“chandelier”. Watching the glass chandelier of the church move to and fro in the
wind, Galileo realized that a simplified form of the pendulum could be used to keep
time.

57. 5.7.1. The pendulum
A pendulum is a heavy bob suspended by a light thread. The length [L] of the
pendulum is measured from the point of suspension or pivot to the centre of gravity
of the bob. When the pendulum is displaced from the centre position and released, it
begins to swing to and fro. One complete to and fro motion is called an oscillation. The
maximum displacement of the bob from the mean position is called the amplitude of
the oscillation. The time taken for one oscillation is called the time period
of the pendulum (T).
The time period of the pendulum:
ƒƒ * It does not depend on the amplitude and this can be verified
experimentally. i s proportional to the square root of the length of the pendulum.
[ Tα√L].
ƒƒi s inversely proportional to the square
root of the acceleration due to gravity.
[ Tα ].
Putting both together along with the
constant of proportionality, 2π, we get the
final form of the formula:

58. 5.7.2. Clocks
Sundial
Water clock
Sand clock
5.7.3. Another characteristic of instruments
-Accuracy
5.7.4. Atomic clock

59. THANK YOU