Units & Measurement Class 11 Notes Physics Chapter 1

 Page 1


 
                                                 
 
Physics 
Units and Measurements 
 
Physical quantities: The quantities that describe the physics laws are called 
physical quantities. In physics, a physical quantity is defined as a system that can 
be quantified and measured using numbers. A physical quantity is completely 
specified if it has: 
? Numerical value only 
Example: Ratio, refractive index, dielectric constant etc. 
? Magnitude only 
Example: Scalars, length, mass etc. 
? Both magnitude and direction 
Example: Vectors, displacement, torque etc. 
In general, expressing the magnitude of a physical quantity, we choose a unit and 
how many times that unit is contained in the physical quantity. 
Types: 
? Fundamental quantities:  
o The quantities not depend on other quantities for complete definition 
are called fundamental quantities. 
o Length, mass, time, electric current, temperature, amount of 
substance and luminous intensity are the seven fundamental 
quantities. 
? Derived quantities:  
o The quantities derived from the base or fundamental quantities are 
called derived quantities. 
o Speed, velocity, electric field etc. are some examples. 
o For example: we define speed to be 
distance
speed = 
time
  i.e. it is 
derived from two fundamental quantities distance and time. 
Similarly, we can derive a derived quantity from two or more 
fundamental quantities. 
 
Unit and its characteristics: 
A unit is the quantity of a constant magnitude used to measure the magnitude of 
other quantities holding the same behaviour. 
Page 2


 
                                                 
 
Physics 
Units and Measurements 
 
Physical quantities: The quantities that describe the physics laws are called 
physical quantities. In physics, a physical quantity is defined as a system that can 
be quantified and measured using numbers. A physical quantity is completely 
specified if it has: 
? Numerical value only 
Example: Ratio, refractive index, dielectric constant etc. 
? Magnitude only 
Example: Scalars, length, mass etc. 
? Both magnitude and direction 
Example: Vectors, displacement, torque etc. 
In general, expressing the magnitude of a physical quantity, we choose a unit and 
how many times that unit is contained in the physical quantity. 
Types: 
? Fundamental quantities:  
o The quantities not depend on other quantities for complete definition 
are called fundamental quantities. 
o Length, mass, time, electric current, temperature, amount of 
substance and luminous intensity are the seven fundamental 
quantities. 
? Derived quantities:  
o The quantities derived from the base or fundamental quantities are 
called derived quantities. 
o Speed, velocity, electric field etc. are some examples. 
o For example: we define speed to be 
distance
speed = 
time
  i.e. it is 
derived from two fundamental quantities distance and time. 
Similarly, we can derive a derived quantity from two or more 
fundamental quantities. 
 
Unit and its characteristics: 
A unit is the quantity of a constant magnitude used to measure the magnitude of 
other quantities holding the same behaviour. 
 
                                                 
The magnitude of a physical quantity is expressed as  
physicalquantity=(numerical) (unit) ?  
? It should be of convenient size. 
? It should be well defined. 
? It should be easily available so that as many laboratories duplicate it. 
? It should not change with time and place. 
? It should not change with the change in physical conditions. 
? It should be universally agreed upon so that results obtained in different 
situations are comparable. 
 
Fundamental and Derived units: 
? Fundamental units: The units chosen for measuring fundamental 
quantities are known as fundamental units. 
Example: kilogram, metre etc. 
? Derived units: The units expressed in terms of the base units are called 
derived units. 
Example: speed, energy etc. 
 
System of units: A complete set of fundamental and derived for all kinds of 
physical quantities is called a system of units.  
A few common systems are 
? CGS (centimetre-gram-second) system: 
This system is based on a variant of the metric system based on the 
centimetre as the unit of length, the gram as the unit of mass, and the second 
as the unit of time. 
? FPS (foot-pound-second) system: 
This system is based on a variant of the metric system based on the foot as 
the unit of length, the pound as the unit of mass, and the second as the unit 
of time. 
? MKS (metre-kilogram-second) system: 
This system is based on a variant of the metric system based on the metre 
as the unit of length, the kilogram as the unit of mass, and the second as 
the unit of time. 
 
An international system of units (SI):  
Page 3


 
                                                 
 
Physics 
Units and Measurements 
 
Physical quantities: The quantities that describe the physics laws are called 
physical quantities. In physics, a physical quantity is defined as a system that can 
be quantified and measured using numbers. A physical quantity is completely 
specified if it has: 
? Numerical value only 
Example: Ratio, refractive index, dielectric constant etc. 
? Magnitude only 
Example: Scalars, length, mass etc. 
? Both magnitude and direction 
Example: Vectors, displacement, torque etc. 
In general, expressing the magnitude of a physical quantity, we choose a unit and 
how many times that unit is contained in the physical quantity. 
Types: 
? Fundamental quantities:  
o The quantities not depend on other quantities for complete definition 
are called fundamental quantities. 
o Length, mass, time, electric current, temperature, amount of 
substance and luminous intensity are the seven fundamental 
quantities. 
? Derived quantities:  
o The quantities derived from the base or fundamental quantities are 
called derived quantities. 
o Speed, velocity, electric field etc. are some examples. 
o For example: we define speed to be 
distance
speed = 
time
  i.e. it is 
derived from two fundamental quantities distance and time. 
Similarly, we can derive a derived quantity from two or more 
fundamental quantities. 
 
Unit and its characteristics: 
A unit is the quantity of a constant magnitude used to measure the magnitude of 
other quantities holding the same behaviour. 
 
                                                 
The magnitude of a physical quantity is expressed as  
physicalquantity=(numerical) (unit) ?  
? It should be of convenient size. 
? It should be well defined. 
? It should be easily available so that as many laboratories duplicate it. 
? It should not change with time and place. 
? It should not change with the change in physical conditions. 
? It should be universally agreed upon so that results obtained in different 
situations are comparable. 
 
Fundamental and Derived units: 
? Fundamental units: The units chosen for measuring fundamental 
quantities are known as fundamental units. 
Example: kilogram, metre etc. 
? Derived units: The units expressed in terms of the base units are called 
derived units. 
Example: speed, energy etc. 
 
System of units: A complete set of fundamental and derived for all kinds of 
physical quantities is called a system of units.  
A few common systems are 
? CGS (centimetre-gram-second) system: 
This system is based on a variant of the metric system based on the 
centimetre as the unit of length, the gram as the unit of mass, and the second 
as the unit of time. 
? FPS (foot-pound-second) system: 
This system is based on a variant of the metric system based on the foot as 
the unit of length, the pound as the unit of mass, and the second as the unit 
of time. 
? MKS (metre-kilogram-second) system: 
This system is based on a variant of the metric system based on the metre 
as the unit of length, the kilogram as the unit of mass, and the second as 
the unit of time. 
 
An international system of units (SI):  
 
                                                 
The system of units that is internationally accepted for measurement is 
abbreviated as SI units.  
They are: 
 
Physical quantity Name of the unit Symbol 
Length metre m 
Mass kilogram kg 
Time second s 
Electric current ampere A 
Temperature kelvin K 
Amount of substance mole mol 
Luminous intensity candela cd 
Plane angle radian rad 
Solid angle Steradian sr 
Radian and steradian: 
? Radian is the angle subtended at the centre of a circle by an arc equal in 
length to the radius of the circle. 
? Steradian is the solid angle subtended at the centre of a sphere by that 
sphere's surface, which is equal in area to the square of the sphere's radius. 
Practical units: 
Practical Units Values 
1AU 
11
1.496 10   m ? 
1 light-year 
15
9.46 10   m ? 
1 parsec 
16
3.08 10   m ? 
1 micron 
6
10   m
?
 
1 angstrom 
10
10   m
?
 
1 fermi 
15
10   m
?
 
1 amu 
27
1.66 10   m
?
? 
1 lunar month 29.5 days 
1 solar day 86400 s 
Page 4


 
                                                 
 
Physics 
Units and Measurements 
 
Physical quantities: The quantities that describe the physics laws are called 
physical quantities. In physics, a physical quantity is defined as a system that can 
be quantified and measured using numbers. A physical quantity is completely 
specified if it has: 
? Numerical value only 
Example: Ratio, refractive index, dielectric constant etc. 
? Magnitude only 
Example: Scalars, length, mass etc. 
? Both magnitude and direction 
Example: Vectors, displacement, torque etc. 
In general, expressing the magnitude of a physical quantity, we choose a unit and 
how many times that unit is contained in the physical quantity. 
Types: 
? Fundamental quantities:  
o The quantities not depend on other quantities for complete definition 
are called fundamental quantities. 
o Length, mass, time, electric current, temperature, amount of 
substance and luminous intensity are the seven fundamental 
quantities. 
? Derived quantities:  
o The quantities derived from the base or fundamental quantities are 
called derived quantities. 
o Speed, velocity, electric field etc. are some examples. 
o For example: we define speed to be 
distance
speed = 
time
  i.e. it is 
derived from two fundamental quantities distance and time. 
Similarly, we can derive a derived quantity from two or more 
fundamental quantities. 
 
Unit and its characteristics: 
A unit is the quantity of a constant magnitude used to measure the magnitude of 
other quantities holding the same behaviour. 
 
                                                 
The magnitude of a physical quantity is expressed as  
physicalquantity=(numerical) (unit) ?  
? It should be of convenient size. 
? It should be well defined. 
? It should be easily available so that as many laboratories duplicate it. 
? It should not change with time and place. 
? It should not change with the change in physical conditions. 
? It should be universally agreed upon so that results obtained in different 
situations are comparable. 
 
Fundamental and Derived units: 
? Fundamental units: The units chosen for measuring fundamental 
quantities are known as fundamental units. 
Example: kilogram, metre etc. 
? Derived units: The units expressed in terms of the base units are called 
derived units. 
Example: speed, energy etc. 
 
System of units: A complete set of fundamental and derived for all kinds of 
physical quantities is called a system of units.  
A few common systems are 
? CGS (centimetre-gram-second) system: 
This system is based on a variant of the metric system based on the 
centimetre as the unit of length, the gram as the unit of mass, and the second 
as the unit of time. 
? FPS (foot-pound-second) system: 
This system is based on a variant of the metric system based on the foot as 
the unit of length, the pound as the unit of mass, and the second as the unit 
of time. 
? MKS (metre-kilogram-second) system: 
This system is based on a variant of the metric system based on the metre 
as the unit of length, the kilogram as the unit of mass, and the second as 
the unit of time. 
 
An international system of units (SI):  
 
                                                 
The system of units that is internationally accepted for measurement is 
abbreviated as SI units.  
They are: 
 
Physical quantity Name of the unit Symbol 
Length metre m 
Mass kilogram kg 
Time second s 
Electric current ampere A 
Temperature kelvin K 
Amount of substance mole mol 
Luminous intensity candela cd 
Plane angle radian rad 
Solid angle Steradian sr 
Radian and steradian: 
? Radian is the angle subtended at the centre of a circle by an arc equal in 
length to the radius of the circle. 
? Steradian is the solid angle subtended at the centre of a sphere by that 
sphere's surface, which is equal in area to the square of the sphere's radius. 
Practical units: 
Practical Units Values 
1AU 
11
1.496 10   m ? 
1 light-year 
15
9.46 10   m ? 
1 parsec 
16
3.08 10   m ? 
1 micron 
6
10   m
?
 
1 angstrom 
10
10   m
?
 
1 fermi 
15
10   m
?
 
1 amu 
27
1.66 10   m
?
? 
1 lunar month 29.5 days 
1 solar day 86400 s 
 
                                                 
Conversion factors: 
? To convert a physical quantity from one set of units to the other, the 
required multiplication factor is the conversion factor. 
? Magnitude of a physical quantity = numerical quantity*unit 
? It means that the numerical value of a physical quantity is inversely 
proportional to the base unit. 
Example: 1m = 100cm = 3.28ft = 39.4inch 
 
Dimensional analysis: 
? Dimensions of a physical quantity are the powers to which the base 
quantities are raised to represent the quantity. 
? Dimensional formula of any physical quantity is that expression which 
represents how and which of the basic quantities with appropriate powers 
in square brackets. 
? The equation obtained by equating a physical quantity with its dimensional 
formula is called a dimensional equation. 
 
Examples: 
 Displacement 
 Velocity 
 Time 
? 
1
 Dimension of length 
 Dimension of time 
v LT
?
?? 
 
Other examples: 
 
Page 5


 
                                                 
 
Physics 
Units and Measurements 
 
Physical quantities: The quantities that describe the physics laws are called 
physical quantities. In physics, a physical quantity is defined as a system that can 
be quantified and measured using numbers. A physical quantity is completely 
specified if it has: 
? Numerical value only 
Example: Ratio, refractive index, dielectric constant etc. 
? Magnitude only 
Example: Scalars, length, mass etc. 
? Both magnitude and direction 
Example: Vectors, displacement, torque etc. 
In general, expressing the magnitude of a physical quantity, we choose a unit and 
how many times that unit is contained in the physical quantity. 
Types: 
? Fundamental quantities:  
o The quantities not depend on other quantities for complete definition 
are called fundamental quantities. 
o Length, mass, time, electric current, temperature, amount of 
substance and luminous intensity are the seven fundamental 
quantities. 
? Derived quantities:  
o The quantities derived from the base or fundamental quantities are 
called derived quantities. 
o Speed, velocity, electric field etc. are some examples. 
o For example: we define speed to be 
distance
speed = 
time
  i.e. it is 
derived from two fundamental quantities distance and time. 
Similarly, we can derive a derived quantity from two or more 
fundamental quantities. 
 
Unit and its characteristics: 
A unit is the quantity of a constant magnitude used to measure the magnitude of 
other quantities holding the same behaviour. 
 
                                                 
The magnitude of a physical quantity is expressed as  
physicalquantity=(numerical) (unit) ?  
? It should be of convenient size. 
? It should be well defined. 
? It should be easily available so that as many laboratories duplicate it. 
? It should not change with time and place. 
? It should not change with the change in physical conditions. 
? It should be universally agreed upon so that results obtained in different 
situations are comparable. 
 
Fundamental and Derived units: 
? Fundamental units: The units chosen for measuring fundamental 
quantities are known as fundamental units. 
Example: kilogram, metre etc. 
? Derived units: The units expressed in terms of the base units are called 
derived units. 
Example: speed, energy etc. 
 
System of units: A complete set of fundamental and derived for all kinds of 
physical quantities is called a system of units.  
A few common systems are 
? CGS (centimetre-gram-second) system: 
This system is based on a variant of the metric system based on the 
centimetre as the unit of length, the gram as the unit of mass, and the second 
as the unit of time. 
? FPS (foot-pound-second) system: 
This system is based on a variant of the metric system based on the foot as 
the unit of length, the pound as the unit of mass, and the second as the unit 
of time. 
? MKS (metre-kilogram-second) system: 
This system is based on a variant of the metric system based on the metre 
as the unit of length, the kilogram as the unit of mass, and the second as 
the unit of time. 
 
An international system of units (SI):  
 
                                                 
The system of units that is internationally accepted for measurement is 
abbreviated as SI units.  
They are: 
 
Physical quantity Name of the unit Symbol 
Length metre m 
Mass kilogram kg 
Time second s 
Electric current ampere A 
Temperature kelvin K 
Amount of substance mole mol 
Luminous intensity candela cd 
Plane angle radian rad 
Solid angle Steradian sr 
Radian and steradian: 
? Radian is the angle subtended at the centre of a circle by an arc equal in 
length to the radius of the circle. 
? Steradian is the solid angle subtended at the centre of a sphere by that 
sphere's surface, which is equal in area to the square of the sphere's radius. 
Practical units: 
Practical Units Values 
1AU 
11
1.496 10   m ? 
1 light-year 
15
9.46 10   m ? 
1 parsec 
16
3.08 10   m ? 
1 micron 
6
10   m
?
 
1 angstrom 
10
10   m
?
 
1 fermi 
15
10   m
?
 
1 amu 
27
1.66 10   m
?
? 
1 lunar month 29.5 days 
1 solar day 86400 s 
 
                                                 
Conversion factors: 
? To convert a physical quantity from one set of units to the other, the 
required multiplication factor is the conversion factor. 
? Magnitude of a physical quantity = numerical quantity*unit 
? It means that the numerical value of a physical quantity is inversely 
proportional to the base unit. 
Example: 1m = 100cm = 3.28ft = 39.4inch 
 
Dimensional analysis: 
? Dimensions of a physical quantity are the powers to which the base 
quantities are raised to represent the quantity. 
? Dimensional formula of any physical quantity is that expression which 
represents how and which of the basic quantities with appropriate powers 
in square brackets. 
? The equation obtained by equating a physical quantity with its dimensional 
formula is called a dimensional equation. 
 
Examples: 
 Displacement 
 Velocity 
 Time 
? 
1
 Dimension of length 
 Dimension of time 
v LT
?
?? 
 
Other examples: 
 
 
                                                 
Physical Quantity Dimensional Formula SI Unit 
Area 
2
L 
2
m 
Volume 
3
L 
3
m 
Density 
3
ML
?
 
3
kgm
?
 
Frequency 
1
T
?
 
Hz or 
1
s
?
 
Speed/Velocity 
1
LT
?
 
1
ms
?
 
Force 
2
MLT
?
 
N 
Acceleration 
2
LT
?
 
2
ms
?
 
Strain 
0 0 0
M LT 
No units 
Surface tension 
2
MT
?
 
1
Nm
?
 
Torque 
22
MLT
?
 
1
Nm  
Critical velocity 
1
LT
?
 
1
ms
?
  
Specific heat capacity 
2 2 1
LT K
??
 
11
Jkg K
??
  
Electric field 
31
MLT A
??
 
1
NC
?
  
Inductance 
2 2 2
MLT A
??
 
H or Henry  
Fluid flow rate 
31
LT
?
 
31
ms
?
 
 
Note: Other units are derived from their respective formulas 
 
Applications: 
? To check the dimensional correctness of a given physical relation. 
? To convert a physical quantity from one system of units to the other 
Example: 
Pressure is given by the formula 
F
P
A
?  
Thus the dimensional formula of pressure is 
2
12
2
F MLT
P ML T
A
L
?
??
? ? ?  
In SI units, 1 Pascal =
2
kgms
?
 . 
In CGS units, 1 Pascal =
2
gcms
?
 .