CHAPTER ONE
UNITS AND MEASUREMENT
1.1 INTRODUCTION
Measurement of any physical quantity involves comparison
with a certain basic, arbitrarily chosen, internationally
accepted reference standard called unit. The result of a
1.1 Introduction measurement of a physical quantity is expressed by a
1.2 The international system of number (or numerical measure) accompanied by a unit.
units Although the number of physical quantities appears to be
1.3 Significant figures very large, we need only a limited number of units for
expressing all the physical quantities, since they are inter-
1.4 Dimensions of physical related with one another. The units for the fundamental or
quantities base quantities are called fundamental or base units. The
1.5 Dimensional formulae and units of all other physical quantities can be expressed as
dimensional equations combinations of the base units. Such units obtained for the
1.6 Dimensional analysis and its derived quantities are called derived units. A complete set
applications of these units, both the base units and derived units, is
known as the system of units.
Summary
Exercises 1.2 THE INTERNATIONAL SYSTEM OF UNITS
In earlier time scientists of different countries were using
different systems of units for measurement. Three such
systems, the CGS, the FPS (or British) system and the MKS
system were in use extensively till recently.
The base units for length, mass and time in these systems
were as follows :
• In CGS system they were centimetre, gram and second
respectively.
• In FPS system they were foot, pound and second
respectively.
• In MKS system they were metre, kilogram and second
respectively.
The system of units which is at present internationally
accepted for measurement is the Système Internationale
d’ Unites (French for International System of Units),
abbreviated as SI. The SI, with standard scheme of symbols,
units and abbreviations, developed by the Bureau
International des Poids et measures (The International
Bureau of Weights and Measures, BIPM) in 1971 were
recently revised by the General Conference on Weights and
Measures in November 2018. The scheme is now for
Buy latest Educart Books on Amazon - https://amzn.to/399Osrj
Rationalised-2023-24
, 2 PHYSICS
international usage in scientific, technical, industrial
and commercial work. Because SI units used decimal
system, conversions within the system are quite simple
and convenient. We shall follow the SI units in
this book.
In SI, there are seven base units as given in (a)
Table 1.1. Besides the seven base units, there are two
more units that are defined for (a) plane angle dθ as the
ratio of length of arc ds to the radius r and (b) solid
angle dΩ as the ratio of the intercepted area dA of the
spherical surface, described about the apex O as the
centre, to the square of its radius r, as shown in
Fig. 1.1(a) and (b) respectively. The unit for plane angle
(b)
is radian with the symbol rad and the unit for the solid
angle is steradian with the symbol sr. Both these are Fig. 1.1 Description of (a) plane angle dθ and
dimensionless quantities. (b) solid angle dΩ .
Table 1.1 SI Base Quantities and Units*
Base SI Units
quantity Name Symbol Definition
Length metre m The metre, symbol m, is the SI unit of length. It is defined by taking the
fixed numerical value of the speed of light in vacuum c to be 299792458
when expressed in the unit m s–1 , where the second is defined in terms of
the caesium frequency ∆ν cs.
Mass kilogram kg The kilogram, symbol kg, is the SI unit of mass. It is defined by taking the
fixed numerical value of the Planck constant h to be 6.62607015×10–34 when
expressed in the unit J s, which is equal to kg m2 s–1, where the metre and
the second are defined in terms of c and ∆ν cs.
Time second s The second, symbol s, is the SI unit of time. It is defined by taking the fixed
numerical value of the caesium frequency ∆ν cs, the unperturbed ground-
state hyperfine transition frequency of the caesium-133 atom, to be
9192631770 when expressed in the unit Hz, which is equal to s–1.
Electric ampere A The ampere, symbol A, is the SI unit of electric current. It is defined by
taking the fixed numerical value of the elementary charge e to be
1.602176634×10–19 when expressed in the unit C, which is equal to A s,
where the second is defined in terms of ∆ν cs.
Thermo kelvin K The kelvin, symbol K, is the SI unit of thermodynamic temperature.
dynamic It is defined by taking the fixed numerical value of the Boltzmann constant
Temperature k to be 1.380649×10–23 when expressed in the unit J K–1, which is equal to
kg m2 s–2 k–1, where the kilogram, metre and second are defined in terms of
h, c and ∆ν cs.
Amount of mole mol The mole, symbol mol, is the SI unit of amount of substance. One mole
substance contains exactly 6.02214076×1023 elementary entities. This number is the
fixed numerical value of the Avogadro constant, NA, when expressed in the
unit mol–1 and is called the Avogadro number. The amount of substance,
symbol n, of a system is a measure of the number of specified elementary
entities. An elementary entity may be an atom, a molecule, an ion, an electron,
any other particle or specified group of particles.
Luminous candela cd The candela, symbol cd, is the SI unit of luminous intensity in given direction.
intensity It is defined by taking the fixed numerical value of the luminous efficacy of
monochromatic radiation of frequency 540×1012 Hz, Kcd, to be 683 when expressed
in the unit lm W–1, which is equal to cd sr W–1, or cd sr kg–1m–2s3, where the
kilogram, metre and second are defined in terms of h, c and ∆ν cs.
* The values mentioned here need not be remembered or asked in a test. They are given here only to indicate the
extent of accuracy to which they are measured. With progress in technology, the measuring techniques get
improved leading to measurements with greater precision. The definitions of base units are revised to keep up
with this progress.
Buy latest Educart Books on Amazon - https://amzn.to/399Osrj
Rationalised-2023-24
UNITS AND MEASUREMENT
1.1 INTRODUCTION
Measurement of any physical quantity involves comparison
with a certain basic, arbitrarily chosen, internationally
accepted reference standard called unit. The result of a
1.1 Introduction measurement of a physical quantity is expressed by a
1.2 The international system of number (or numerical measure) accompanied by a unit.
units Although the number of physical quantities appears to be
1.3 Significant figures very large, we need only a limited number of units for
expressing all the physical quantities, since they are inter-
1.4 Dimensions of physical related with one another. The units for the fundamental or
quantities base quantities are called fundamental or base units. The
1.5 Dimensional formulae and units of all other physical quantities can be expressed as
dimensional equations combinations of the base units. Such units obtained for the
1.6 Dimensional analysis and its derived quantities are called derived units. A complete set
applications of these units, both the base units and derived units, is
known as the system of units.
Summary
Exercises 1.2 THE INTERNATIONAL SYSTEM OF UNITS
In earlier time scientists of different countries were using
different systems of units for measurement. Three such
systems, the CGS, the FPS (or British) system and the MKS
system were in use extensively till recently.
The base units for length, mass and time in these systems
were as follows :
• In CGS system they were centimetre, gram and second
respectively.
• In FPS system they were foot, pound and second
respectively.
• In MKS system they were metre, kilogram and second
respectively.
The system of units which is at present internationally
accepted for measurement is the Système Internationale
d’ Unites (French for International System of Units),
abbreviated as SI. The SI, with standard scheme of symbols,
units and abbreviations, developed by the Bureau
International des Poids et measures (The International
Bureau of Weights and Measures, BIPM) in 1971 were
recently revised by the General Conference on Weights and
Measures in November 2018. The scheme is now for
Buy latest Educart Books on Amazon - https://amzn.to/399Osrj
Rationalised-2023-24
, 2 PHYSICS
international usage in scientific, technical, industrial
and commercial work. Because SI units used decimal
system, conversions within the system are quite simple
and convenient. We shall follow the SI units in
this book.
In SI, there are seven base units as given in (a)
Table 1.1. Besides the seven base units, there are two
more units that are defined for (a) plane angle dθ as the
ratio of length of arc ds to the radius r and (b) solid
angle dΩ as the ratio of the intercepted area dA of the
spherical surface, described about the apex O as the
centre, to the square of its radius r, as shown in
Fig. 1.1(a) and (b) respectively. The unit for plane angle
(b)
is radian with the symbol rad and the unit for the solid
angle is steradian with the symbol sr. Both these are Fig. 1.1 Description of (a) plane angle dθ and
dimensionless quantities. (b) solid angle dΩ .
Table 1.1 SI Base Quantities and Units*
Base SI Units
quantity Name Symbol Definition
Length metre m The metre, symbol m, is the SI unit of length. It is defined by taking the
fixed numerical value of the speed of light in vacuum c to be 299792458
when expressed in the unit m s–1 , where the second is defined in terms of
the caesium frequency ∆ν cs.
Mass kilogram kg The kilogram, symbol kg, is the SI unit of mass. It is defined by taking the
fixed numerical value of the Planck constant h to be 6.62607015×10–34 when
expressed in the unit J s, which is equal to kg m2 s–1, where the metre and
the second are defined in terms of c and ∆ν cs.
Time second s The second, symbol s, is the SI unit of time. It is defined by taking the fixed
numerical value of the caesium frequency ∆ν cs, the unperturbed ground-
state hyperfine transition frequency of the caesium-133 atom, to be
9192631770 when expressed in the unit Hz, which is equal to s–1.
Electric ampere A The ampere, symbol A, is the SI unit of electric current. It is defined by
taking the fixed numerical value of the elementary charge e to be
1.602176634×10–19 when expressed in the unit C, which is equal to A s,
where the second is defined in terms of ∆ν cs.
Thermo kelvin K The kelvin, symbol K, is the SI unit of thermodynamic temperature.
dynamic It is defined by taking the fixed numerical value of the Boltzmann constant
Temperature k to be 1.380649×10–23 when expressed in the unit J K–1, which is equal to
kg m2 s–2 k–1, where the kilogram, metre and second are defined in terms of
h, c and ∆ν cs.
Amount of mole mol The mole, symbol mol, is the SI unit of amount of substance. One mole
substance contains exactly 6.02214076×1023 elementary entities. This number is the
fixed numerical value of the Avogadro constant, NA, when expressed in the
unit mol–1 and is called the Avogadro number. The amount of substance,
symbol n, of a system is a measure of the number of specified elementary
entities. An elementary entity may be an atom, a molecule, an ion, an electron,
any other particle or specified group of particles.
Luminous candela cd The candela, symbol cd, is the SI unit of luminous intensity in given direction.
intensity It is defined by taking the fixed numerical value of the luminous efficacy of
monochromatic radiation of frequency 540×1012 Hz, Kcd, to be 683 when expressed
in the unit lm W–1, which is equal to cd sr W–1, or cd sr kg–1m–2s3, where the
kilogram, metre and second are defined in terms of h, c and ∆ν cs.
* The values mentioned here need not be remembered or asked in a test. They are given here only to indicate the
extent of accuracy to which they are measured. With progress in technology, the measuring techniques get
improved leading to measurements with greater precision. The definitions of base units are revised to keep up
with this progress.
Buy latest Educart Books on Amazon - https://amzn.to/399Osrj
Rationalised-2023-24
