Unit-I Units and Measurements 2023-2024 PUC-I
Unit-I Chapter-01 UNITS AND MEASUREMENTS Hrs: 04 Marks: 03
1.1 Introduction
Physical quantities: The quantities which can be measured and expressed in terms
of numerical values are called physical quantities.
Example: Length, mass, time, force, work, energy, etc.
Fundamental or base physical quantities: The physical quantities which are expressed
independently are called base physical quantities.
Example: Length, mass, time, temperature, electric current, etc.
Derived physical quantities: The physical quantities which can be obtained from
fundamental or base quantities are called derived quantities.
𝑀𝑎𝑠𝑠
Example: 𝐴𝑟𝑒𝑎 = 𝑙𝑒𝑛𝑔𝑡ℎ 𝑋 𝑙𝑒𝑛𝑔𝑡ℎ, 𝑉𝑜𝑙𝑢𝑚𝑒 = (𝑙𝑒𝑛𝑔𝑡ℎ)3 , 𝐷𝑒𝑛𝑠𝑖𝑡𝑦 = 𝑉𝑜𝑙𝑢𝑚𝑒 ,
𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝐷𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡
𝑆𝑝𝑒𝑒𝑑 = , 𝐴𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 = (𝑇𝑖𝑚𝑒)2
, 𝐹𝑜𝑟𝑐𝑒 = 𝑀𝑎𝑠𝑠 𝑋 𝐴𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 etc.
𝑇𝑖𝑚𝑒
Measurement: Measurement means comparison of given physical quantity with some
standard quantity.
Unit: The standard quantity used for the measurement of physical quantity is called a unit.
Example: The unit of Length Mass, Time, Area, Volume, Density, etc.
Fundamental or base unit:
The units of base physical quantities are called base units.
Example: The units of length mass time electric current temperature etc are called fundamental
units or base units.
Derived units: The units of derived quantities which can be obtained from fundamental or
base units are called derived units.
Example: The unit of Area, Volume, Density, Speed, Acceleration, Force,
Momentum, Work etc.
Features of unit:
➢ If must be of suitable size.
➢ It must be accurately defined.
➢ It must be easily reproducible.
➢ It should not be change with time and physical conditions like temperature, pressure.
Prof: Venugopal H. R. MSc,MPhil,B.Ed; Lecturer in Physics P C Jabin PU College of Science, Hubballi-31 Page 1
, Unit-I Units and Measurements 2023-2024 PUC-I
System of units: The complete set of units used for measurement of both base and derived
units for all kind of physical quantities is called system of units.
Fundamental system of units:
Units for
System
Length Mass Time
C.G.S centimetre (cm) gram (g) Second (s)
F.P.S Foot (ft) Pound (lb) Second (s)
M.K.S metre (m) Kilogram (kg) Second (s)
1.2 International system of units (SI):
In 1971, the general conference on weights and measures decided to use MKS system by
adding four more fundamental quantities. This system at present internationally accepted
for measurement which is called SI system.
S I system is abbreviated as Systeme of internationale d’ unites.
The SI system consists of seven fundamental quantities such as length, mass, time, current,
temperature, luminous intensity and amount of substance. Also, it has two supplementary
units called plane angle and solid angle.
The units of base quantities in SI system are given below.
Sl.No. Base quantity SI units Symbol
1 Length metre m
2 Mass kilogram Kg
3 Time second S
4 Electric current ampere A
5 Temperature kelvin K
6 Luminous intensity candela cd
7 Amount of substance mole mol
Sl.No. Supplementary quantity Supplementary units Symbol
1 Plane angle radian rad
2 Solid angle steradian sr
The radian: One radian is the angle subtended at the centre of a circle by an arc equal in
length to the radius of the circle.
If an arc of length 𝑑𝑠 subtends an angle 𝑑𝜃 at the centre 𝑂 of a circle of
radius 𝑟 then
𝑎𝑟𝑐 𝑙𝑒𝑛𝑔𝑡ℎ 𝑑𝑆
𝑑𝜃 = 𝑑𝜃 = radian
𝑟𝑎𝑑𝑖𝑢𝑠 𝑟
Steradian (Sr): One steradian is the solid angle subtended at the center of a sphere by its
surface whose area is equal to the square of the radius of the sphere.
Prof: Venugopal H. R. MSc,MPhil,B.Ed; Lecturer in Physics P C Jabin PU College of Science, Hubballi-31 Page 2
Unit-I Chapter-01 UNITS AND MEASUREMENTS Hrs: 04 Marks: 03
1.1 Introduction
Physical quantities: The quantities which can be measured and expressed in terms
of numerical values are called physical quantities.
Example: Length, mass, time, force, work, energy, etc.
Fundamental or base physical quantities: The physical quantities which are expressed
independently are called base physical quantities.
Example: Length, mass, time, temperature, electric current, etc.
Derived physical quantities: The physical quantities which can be obtained from
fundamental or base quantities are called derived quantities.
𝑀𝑎𝑠𝑠
Example: 𝐴𝑟𝑒𝑎 = 𝑙𝑒𝑛𝑔𝑡ℎ 𝑋 𝑙𝑒𝑛𝑔𝑡ℎ, 𝑉𝑜𝑙𝑢𝑚𝑒 = (𝑙𝑒𝑛𝑔𝑡ℎ)3 , 𝐷𝑒𝑛𝑠𝑖𝑡𝑦 = 𝑉𝑜𝑙𝑢𝑚𝑒 ,
𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝐷𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡
𝑆𝑝𝑒𝑒𝑑 = , 𝐴𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 = (𝑇𝑖𝑚𝑒)2
, 𝐹𝑜𝑟𝑐𝑒 = 𝑀𝑎𝑠𝑠 𝑋 𝐴𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 etc.
𝑇𝑖𝑚𝑒
Measurement: Measurement means comparison of given physical quantity with some
standard quantity.
Unit: The standard quantity used for the measurement of physical quantity is called a unit.
Example: The unit of Length Mass, Time, Area, Volume, Density, etc.
Fundamental or base unit:
The units of base physical quantities are called base units.
Example: The units of length mass time electric current temperature etc are called fundamental
units or base units.
Derived units: The units of derived quantities which can be obtained from fundamental or
base units are called derived units.
Example: The unit of Area, Volume, Density, Speed, Acceleration, Force,
Momentum, Work etc.
Features of unit:
➢ If must be of suitable size.
➢ It must be accurately defined.
➢ It must be easily reproducible.
➢ It should not be change with time and physical conditions like temperature, pressure.
Prof: Venugopal H. R. MSc,MPhil,B.Ed; Lecturer in Physics P C Jabin PU College of Science, Hubballi-31 Page 1
, Unit-I Units and Measurements 2023-2024 PUC-I
System of units: The complete set of units used for measurement of both base and derived
units for all kind of physical quantities is called system of units.
Fundamental system of units:
Units for
System
Length Mass Time
C.G.S centimetre (cm) gram (g) Second (s)
F.P.S Foot (ft) Pound (lb) Second (s)
M.K.S metre (m) Kilogram (kg) Second (s)
1.2 International system of units (SI):
In 1971, the general conference on weights and measures decided to use MKS system by
adding four more fundamental quantities. This system at present internationally accepted
for measurement which is called SI system.
S I system is abbreviated as Systeme of internationale d’ unites.
The SI system consists of seven fundamental quantities such as length, mass, time, current,
temperature, luminous intensity and amount of substance. Also, it has two supplementary
units called plane angle and solid angle.
The units of base quantities in SI system are given below.
Sl.No. Base quantity SI units Symbol
1 Length metre m
2 Mass kilogram Kg
3 Time second S
4 Electric current ampere A
5 Temperature kelvin K
6 Luminous intensity candela cd
7 Amount of substance mole mol
Sl.No. Supplementary quantity Supplementary units Symbol
1 Plane angle radian rad
2 Solid angle steradian sr
The radian: One radian is the angle subtended at the centre of a circle by an arc equal in
length to the radius of the circle.
If an arc of length 𝑑𝑠 subtends an angle 𝑑𝜃 at the centre 𝑂 of a circle of
radius 𝑟 then
𝑎𝑟𝑐 𝑙𝑒𝑛𝑔𝑡ℎ 𝑑𝑆
𝑑𝜃 = 𝑑𝜃 = radian
𝑟𝑎𝑑𝑖𝑢𝑠 𝑟
Steradian (Sr): One steradian is the solid angle subtended at the center of a sphere by its
surface whose area is equal to the square of the radius of the sphere.
Prof: Venugopal H. R. MSc,MPhil,B.Ed; Lecturer in Physics P C Jabin PU College of Science, Hubballi-31 Page 2
