Units & Measurement Class 11 Notes Physics Chapter 1

 Page 1


1 
 
Chapter 1  
UNITS AND DIMENSIONS 
Learning objective:After going through this chapter, students will be able to; 
- understand physical quantities, fundamental and derived; 
- describe different systems of units; 
- define dimensions and formulate dimensional formulae; 
- write dimensionalequations and apply these to verify various formulations. 
 
1.1 DEFINITION OF PHYSICS AND PHYSICAL QUANTITIES  
Physics: Physics is the branch of science, which deals with the study of nature and properties 
of matter and energy. The subject matter of physics includes heat, light, sound, electricity, 
magnetism and the structure of atoms. 
For designing a law of physics, a scientific method is followed which includes the 
verifications with experiments. The physics, attempts are made to measure the quantities with 
the best accuracy.Thus, Physics can also be defined as science of measurement. 
Applied Physics is the application of the Physics to help human beings and solving their 
problem, it is usually considered as a bridge or a connection between Physics & Engineering. 
Physical Quantities: All quantities in terms of which laws of physics can be expressed and 
which can be measured are called Physical Quantities. 
For example; Distance, Speed, Mass, Force etc. 
1.2  UNITS: FUNDAMENTAL AND DERIVED UNITS 
Measurement:  In our daily life, we need to express and compare the magnitude of different 
quantities; this can be done only by measuring them. 
Measurement is the comparison of an unknown physical quantity with a known fixed 
physical quantity. 
Unit: The known fixed physical quantity is called unit.  
OR  
The quantity used as standard for measurement is called unit. 
For example, when we say that length of the class room is 8 metre. We compare the length of 
class room with standard quantity of length called metre. 
Length of class room = 8 metre 
 
Q = nu 
Page 2


1 
 
Chapter 1  
UNITS AND DIMENSIONS 
Learning objective:After going through this chapter, students will be able to; 
- understand physical quantities, fundamental and derived; 
- describe different systems of units; 
- define dimensions and formulate dimensional formulae; 
- write dimensionalequations and apply these to verify various formulations. 
 
1.1 DEFINITION OF PHYSICS AND PHYSICAL QUANTITIES  
Physics: Physics is the branch of science, which deals with the study of nature and properties 
of matter and energy. The subject matter of physics includes heat, light, sound, electricity, 
magnetism and the structure of atoms. 
For designing a law of physics, a scientific method is followed which includes the 
verifications with experiments. The physics, attempts are made to measure the quantities with 
the best accuracy.Thus, Physics can also be defined as science of measurement. 
Applied Physics is the application of the Physics to help human beings and solving their 
problem, it is usually considered as a bridge or a connection between Physics & Engineering. 
Physical Quantities: All quantities in terms of which laws of physics can be expressed and 
which can be measured are called Physical Quantities. 
For example; Distance, Speed, Mass, Force etc. 
1.2  UNITS: FUNDAMENTAL AND DERIVED UNITS 
Measurement:  In our daily life, we need to express and compare the magnitude of different 
quantities; this can be done only by measuring them. 
Measurement is the comparison of an unknown physical quantity with a known fixed 
physical quantity. 
Unit: The known fixed physical quantity is called unit.  
OR  
The quantity used as standard for measurement is called unit. 
For example, when we say that length of the class room is 8 metre. We compare the length of 
class room with standard quantity of length called metre. 
Length of class room = 8 metre 
 
Q = nu 
2 
 
           Physical Quantity = Numerical value × unit 
  Q = Physical Quantity 
  n = Numerical value 
  u = Standard unit 
e.g.    Mass of stool = 15 kg 
 Mass = Physical quantity 
 15 = Numerical value 
 Kg = Standard unit 
Means mass of stool is 15 times of known quantity i.e. Kg. 
Characteristics of Standard Unit: A unit selected for measuring a physical quantity should 
have the following properties 
(i) It should be well defined i.e. its concept should be clear. 
(ii) It should not change with change in physical conditions like temperature, 
pressure, stress etc.. 
(iii) It should be suitable in size; neither too large nor too small. 
(iv) It should not change with place or time. 
(v) It should be reproducible. 
(vi) It should be internationally accepted.                                                                                     
Classification of Units: Units can be classified into two categories. 
• Fundamental  
• Derived 
Fundamental Quantity:The quantity which is independent of other physical quantities. In 
mechanics, mass, length and time are called fundamental quantities. Units of these 
fundamental physical quantities are called Fundamental units. 
e.g.  Fundamental Physical Quantity   Fundamental unit 
   Mass    Kg, Gram, Pound 
   Length    Metre, Centimetre, Foot 
   Time    Second 
Derived Quantity: The quantity which is derived from the fundamental quantities e.g.  area 
is a derived quantity. 
   Area = Length ? Breadth 
    = Length ? Length 
    = (Length)
2
 
   Speed  =Distance / Time 
    =Length / Time 
The units for derived quantities are called Derived Units. 
Page 3


1 
 
Chapter 1  
UNITS AND DIMENSIONS 
Learning objective:After going through this chapter, students will be able to; 
- understand physical quantities, fundamental and derived; 
- describe different systems of units; 
- define dimensions and formulate dimensional formulae; 
- write dimensionalequations and apply these to verify various formulations. 
 
1.1 DEFINITION OF PHYSICS AND PHYSICAL QUANTITIES  
Physics: Physics is the branch of science, which deals with the study of nature and properties 
of matter and energy. The subject matter of physics includes heat, light, sound, electricity, 
magnetism and the structure of atoms. 
For designing a law of physics, a scientific method is followed which includes the 
verifications with experiments. The physics, attempts are made to measure the quantities with 
the best accuracy.Thus, Physics can also be defined as science of measurement. 
Applied Physics is the application of the Physics to help human beings and solving their 
problem, it is usually considered as a bridge or a connection between Physics & Engineering. 
Physical Quantities: All quantities in terms of which laws of physics can be expressed and 
which can be measured are called Physical Quantities. 
For example; Distance, Speed, Mass, Force etc. 
1.2  UNITS: FUNDAMENTAL AND DERIVED UNITS 
Measurement:  In our daily life, we need to express and compare the magnitude of different 
quantities; this can be done only by measuring them. 
Measurement is the comparison of an unknown physical quantity with a known fixed 
physical quantity. 
Unit: The known fixed physical quantity is called unit.  
OR  
The quantity used as standard for measurement is called unit. 
For example, when we say that length of the class room is 8 metre. We compare the length of 
class room with standard quantity of length called metre. 
Length of class room = 8 metre 
 
Q = nu 
2 
 
           Physical Quantity = Numerical value × unit 
  Q = Physical Quantity 
  n = Numerical value 
  u = Standard unit 
e.g.    Mass of stool = 15 kg 
 Mass = Physical quantity 
 15 = Numerical value 
 Kg = Standard unit 
Means mass of stool is 15 times of known quantity i.e. Kg. 
Characteristics of Standard Unit: A unit selected for measuring a physical quantity should 
have the following properties 
(i) It should be well defined i.e. its concept should be clear. 
(ii) It should not change with change in physical conditions like temperature, 
pressure, stress etc.. 
(iii) It should be suitable in size; neither too large nor too small. 
(iv) It should not change with place or time. 
(v) It should be reproducible. 
(vi) It should be internationally accepted.                                                                                     
Classification of Units: Units can be classified into two categories. 
• Fundamental  
• Derived 
Fundamental Quantity:The quantity which is independent of other physical quantities. In 
mechanics, mass, length and time are called fundamental quantities. Units of these 
fundamental physical quantities are called Fundamental units. 
e.g.  Fundamental Physical Quantity   Fundamental unit 
   Mass    Kg, Gram, Pound 
   Length    Metre, Centimetre, Foot 
   Time    Second 
Derived Quantity: The quantity which is derived from the fundamental quantities e.g.  area 
is a derived quantity. 
   Area = Length ? Breadth 
    = Length ? Length 
    = (Length)
2
 
   Speed  =Distance / Time 
    =Length / Time 
The units for derived quantities are called Derived Units. 
3 
 
1.3  SYSTEMS OF UNITS: CGS, FPS, MKS, SI  
For measurement of physical quantities, the following systems are commonly used:- 
(i) C.G.S system:  In this system, the unit of length is centimetre, the unit of mass is 
gram and the unit of time is second. 
(ii) F.P.S system: In this system, the unit of length is foot, the unit of mass is pound and 
the unit of time is second. 
(iii) M.K.S: In this system, the unit of length is metre, unit of mass is kg and the unit of 
time is second. 
(iv) S.I System: This system is an improved and extended version of M.K.S system of 
units. It is called international system of unit. 
 
With the development of science & technology, the three fundamental quantities like 
mass, length & time were not sufficient as many other quantities like electric current, heat 
etc. were introduced. 
Therefore, more fundamental units in addition to the units of mass, length and time 
are required. 
Thus, MKS system was modified with addition of four other fundamental quantities 
and two supplementary quantities.   
Table of Fundamental Units 
Sr. No. Name of Physical Quantity Unit Symbol 
1 
2 
3 
4 
5 
6 
7 
Length 
Mass 
Time 
Temperature 
Electric Current 
Luminous Intensity 
Quantity of Matter 
 
Metre 
Kilogram 
Second 
Kelvin 
Ampere 
Candela 
Mole 
m 
Kg 
s 
K 
A 
Cd 
mol 
 
 
Table of Supplementary unit 
Sr. No Name of Physical Quantity Unit Symbol 
1 
2 
Plane angle 
Solid angle 
Radian 
Steradian 
rad 
sr 
 
Advantage of S.I. system: 
(i) It is coherent system of unit i.e. the derived units of a physical quantities are easily 
obtained by multiplication or division of fundamental units. 
(ii) It is a rational system of units i.e. it uses only one unit for one physical quantity. e.g. 
It uses Joule (J) as unit for all types of energies (heat, light, mechanical). 
(iii) It is metric system of units i.e. it’s multiples & submultiples can be expressed in 
power of 10. 
Page 4


1 
 
Chapter 1  
UNITS AND DIMENSIONS 
Learning objective:After going through this chapter, students will be able to; 
- understand physical quantities, fundamental and derived; 
- describe different systems of units; 
- define dimensions and formulate dimensional formulae; 
- write dimensionalequations and apply these to verify various formulations. 
 
1.1 DEFINITION OF PHYSICS AND PHYSICAL QUANTITIES  
Physics: Physics is the branch of science, which deals with the study of nature and properties 
of matter and energy. The subject matter of physics includes heat, light, sound, electricity, 
magnetism and the structure of atoms. 
For designing a law of physics, a scientific method is followed which includes the 
verifications with experiments. The physics, attempts are made to measure the quantities with 
the best accuracy.Thus, Physics can also be defined as science of measurement. 
Applied Physics is the application of the Physics to help human beings and solving their 
problem, it is usually considered as a bridge or a connection between Physics & Engineering. 
Physical Quantities: All quantities in terms of which laws of physics can be expressed and 
which can be measured are called Physical Quantities. 
For example; Distance, Speed, Mass, Force etc. 
1.2  UNITS: FUNDAMENTAL AND DERIVED UNITS 
Measurement:  In our daily life, we need to express and compare the magnitude of different 
quantities; this can be done only by measuring them. 
Measurement is the comparison of an unknown physical quantity with a known fixed 
physical quantity. 
Unit: The known fixed physical quantity is called unit.  
OR  
The quantity used as standard for measurement is called unit. 
For example, when we say that length of the class room is 8 metre. We compare the length of 
class room with standard quantity of length called metre. 
Length of class room = 8 metre 
 
Q = nu 
2 
 
           Physical Quantity = Numerical value × unit 
  Q = Physical Quantity 
  n = Numerical value 
  u = Standard unit 
e.g.    Mass of stool = 15 kg 
 Mass = Physical quantity 
 15 = Numerical value 
 Kg = Standard unit 
Means mass of stool is 15 times of known quantity i.e. Kg. 
Characteristics of Standard Unit: A unit selected for measuring a physical quantity should 
have the following properties 
(i) It should be well defined i.e. its concept should be clear. 
(ii) It should not change with change in physical conditions like temperature, 
pressure, stress etc.. 
(iii) It should be suitable in size; neither too large nor too small. 
(iv) It should not change with place or time. 
(v) It should be reproducible. 
(vi) It should be internationally accepted.                                                                                     
Classification of Units: Units can be classified into two categories. 
• Fundamental  
• Derived 
Fundamental Quantity:The quantity which is independent of other physical quantities. In 
mechanics, mass, length and time are called fundamental quantities. Units of these 
fundamental physical quantities are called Fundamental units. 
e.g.  Fundamental Physical Quantity   Fundamental unit 
   Mass    Kg, Gram, Pound 
   Length    Metre, Centimetre, Foot 
   Time    Second 
Derived Quantity: The quantity which is derived from the fundamental quantities e.g.  area 
is a derived quantity. 
   Area = Length ? Breadth 
    = Length ? Length 
    = (Length)
2
 
   Speed  =Distance / Time 
    =Length / Time 
The units for derived quantities are called Derived Units. 
3 
 
1.3  SYSTEMS OF UNITS: CGS, FPS, MKS, SI  
For measurement of physical quantities, the following systems are commonly used:- 
(i) C.G.S system:  In this system, the unit of length is centimetre, the unit of mass is 
gram and the unit of time is second. 
(ii) F.P.S system: In this system, the unit of length is foot, the unit of mass is pound and 
the unit of time is second. 
(iii) M.K.S: In this system, the unit of length is metre, unit of mass is kg and the unit of 
time is second. 
(iv) S.I System: This system is an improved and extended version of M.K.S system of 
units. It is called international system of unit. 
 
With the development of science & technology, the three fundamental quantities like 
mass, length & time were not sufficient as many other quantities like electric current, heat 
etc. were introduced. 
Therefore, more fundamental units in addition to the units of mass, length and time 
are required. 
Thus, MKS system was modified with addition of four other fundamental quantities 
and two supplementary quantities.   
Table of Fundamental Units 
Sr. No. Name of Physical Quantity Unit Symbol 
1 
2 
3 
4 
5 
6 
7 
Length 
Mass 
Time 
Temperature 
Electric Current 
Luminous Intensity 
Quantity of Matter 
 
Metre 
Kilogram 
Second 
Kelvin 
Ampere 
Candela 
Mole 
m 
Kg 
s 
K 
A 
Cd 
mol 
 
 
Table of Supplementary unit 
Sr. No Name of Physical Quantity Unit Symbol 
1 
2 
Plane angle 
Solid angle 
Radian 
Steradian 
rad 
sr 
 
Advantage of S.I. system: 
(i) It is coherent system of unit i.e. the derived units of a physical quantities are easily 
obtained by multiplication or division of fundamental units. 
(ii) It is a rational system of units i.e. it uses only one unit for one physical quantity. e.g. 
It uses Joule (J) as unit for all types of energies (heat, light, mechanical). 
(iii) It is metric system of units i.e. it’s multiples & submultiples can be expressed in 
power of 10. 
4 
 
Definition of Basic and Supplementary Unit of S.I. 
1. Metre (m): The metre is the length of the path travelled by light in vacuum during a time 
interval of 1/299 792 458 of a second. 
2. Kilogram (Kg) : The kilogram is the mass of the platinum-iridium prototype which was 
 approved by the ConférenceGénérale des Poids et Mesures, held in Paris in  1889, and kept 
by the Bureau International des Poids et Mesures. 
3. Second (s): The second is the duration of 9192631770 periods of the radiation 
corresponding to the transition between two hyperfine levels of the ground state of Cesium-
133 atom. 
4. Ampere (A) : The ampere is the intensity of a constant current which, if maintained in two 
straight  parallel conductors of infinite length, of negligible circular cross-section, and  placed 
1 metre apart in vacuum, would produce between these conductors a  force equal to 2 ? 10
-
7
Newton per metre of length. 
5. Kelvin (K): Kelvin is the fraction 1/273.16 of the thermodynamic temperature of the triple 
point of water. 
6. Candela (Cd): The candela is the luminous intensity, in a given direction, of a source that 
emits monochromatic radiation of frequency 540 x 10
12
 hertz and that has a radiant intensity 
in that direction of 1/683 watt per steradian. 
7. Mole (mol): The mole is the amount of substance of a system which contains as many 
elementary entities as there are atoms in 0.012 kilogram of Carbon-12. 
Supplementary units: 
1. Radian (rad): It is supplementary unit of plane angle. It is the plane angle subtended 
at the centre of a circle by an arc of the circle equal to the radius of the circle. It is 
denoted by ?? . 
   ?? = l / r;  ?? is length of the arcand ?? is radius of the circle 
2. Steradian (Sr): It is supplementary unit of solid angle. It is the angle subtended at the 
centre of a sphere by a surface area of the sphere having magnitude equal to the 
square of the radius of the sphere. It is denoted by ?. 
? = ?s / r
2
 
SOME IMPORTANT ABBREVIATIONS 
Symbol Prefix Multiplier Symbol Prefix Multiplier 
D 
c 
m 
µ 
n 
Deci 
centi 
milli 
micro 
nano 
10
-1
 
10
-2
 
10
-3
 
10
-6
 
10
-9
 
da 
h 
k 
M 
G 
deca 
hecto 
kilo 
mega 
giga 
10
1
 
10
2
 
10
3
 
10
6
 
10
9
 
Page 5


1 
 
Chapter 1  
UNITS AND DIMENSIONS 
Learning objective:After going through this chapter, students will be able to; 
- understand physical quantities, fundamental and derived; 
- describe different systems of units; 
- define dimensions and formulate dimensional formulae; 
- write dimensionalequations and apply these to verify various formulations. 
 
1.1 DEFINITION OF PHYSICS AND PHYSICAL QUANTITIES  
Physics: Physics is the branch of science, which deals with the study of nature and properties 
of matter and energy. The subject matter of physics includes heat, light, sound, electricity, 
magnetism and the structure of atoms. 
For designing a law of physics, a scientific method is followed which includes the 
verifications with experiments. The physics, attempts are made to measure the quantities with 
the best accuracy.Thus, Physics can also be defined as science of measurement. 
Applied Physics is the application of the Physics to help human beings and solving their 
problem, it is usually considered as a bridge or a connection between Physics & Engineering. 
Physical Quantities: All quantities in terms of which laws of physics can be expressed and 
which can be measured are called Physical Quantities. 
For example; Distance, Speed, Mass, Force etc. 
1.2  UNITS: FUNDAMENTAL AND DERIVED UNITS 
Measurement:  In our daily life, we need to express and compare the magnitude of different 
quantities; this can be done only by measuring them. 
Measurement is the comparison of an unknown physical quantity with a known fixed 
physical quantity. 
Unit: The known fixed physical quantity is called unit.  
OR  
The quantity used as standard for measurement is called unit. 
For example, when we say that length of the class room is 8 metre. We compare the length of 
class room with standard quantity of length called metre. 
Length of class room = 8 metre 
 
Q = nu 
2 
 
           Physical Quantity = Numerical value × unit 
  Q = Physical Quantity 
  n = Numerical value 
  u = Standard unit 
e.g.    Mass of stool = 15 kg 
 Mass = Physical quantity 
 15 = Numerical value 
 Kg = Standard unit 
Means mass of stool is 15 times of known quantity i.e. Kg. 
Characteristics of Standard Unit: A unit selected for measuring a physical quantity should 
have the following properties 
(i) It should be well defined i.e. its concept should be clear. 
(ii) It should not change with change in physical conditions like temperature, 
pressure, stress etc.. 
(iii) It should be suitable in size; neither too large nor too small. 
(iv) It should not change with place or time. 
(v) It should be reproducible. 
(vi) It should be internationally accepted.                                                                                     
Classification of Units: Units can be classified into two categories. 
• Fundamental  
• Derived 
Fundamental Quantity:The quantity which is independent of other physical quantities. In 
mechanics, mass, length and time are called fundamental quantities. Units of these 
fundamental physical quantities are called Fundamental units. 
e.g.  Fundamental Physical Quantity   Fundamental unit 
   Mass    Kg, Gram, Pound 
   Length    Metre, Centimetre, Foot 
   Time    Second 
Derived Quantity: The quantity which is derived from the fundamental quantities e.g.  area 
is a derived quantity. 
   Area = Length ? Breadth 
    = Length ? Length 
    = (Length)
2
 
   Speed  =Distance / Time 
    =Length / Time 
The units for derived quantities are called Derived Units. 
3 
 
1.3  SYSTEMS OF UNITS: CGS, FPS, MKS, SI  
For measurement of physical quantities, the following systems are commonly used:- 
(i) C.G.S system:  In this system, the unit of length is centimetre, the unit of mass is 
gram and the unit of time is second. 
(ii) F.P.S system: In this system, the unit of length is foot, the unit of mass is pound and 
the unit of time is second. 
(iii) M.K.S: In this system, the unit of length is metre, unit of mass is kg and the unit of 
time is second. 
(iv) S.I System: This system is an improved and extended version of M.K.S system of 
units. It is called international system of unit. 
 
With the development of science & technology, the three fundamental quantities like 
mass, length & time were not sufficient as many other quantities like electric current, heat 
etc. were introduced. 
Therefore, more fundamental units in addition to the units of mass, length and time 
are required. 
Thus, MKS system was modified with addition of four other fundamental quantities 
and two supplementary quantities.   
Table of Fundamental Units 
Sr. No. Name of Physical Quantity Unit Symbol 
1 
2 
3 
4 
5 
6 
7 
Length 
Mass 
Time 
Temperature 
Electric Current 
Luminous Intensity 
Quantity of Matter 
 
Metre 
Kilogram 
Second 
Kelvin 
Ampere 
Candela 
Mole 
m 
Kg 
s 
K 
A 
Cd 
mol 
 
 
Table of Supplementary unit 
Sr. No Name of Physical Quantity Unit Symbol 
1 
2 
Plane angle 
Solid angle 
Radian 
Steradian 
rad 
sr 
 
Advantage of S.I. system: 
(i) It is coherent system of unit i.e. the derived units of a physical quantities are easily 
obtained by multiplication or division of fundamental units. 
(ii) It is a rational system of units i.e. it uses only one unit for one physical quantity. e.g. 
It uses Joule (J) as unit for all types of energies (heat, light, mechanical). 
(iii) It is metric system of units i.e. it’s multiples & submultiples can be expressed in 
power of 10. 
4 
 
Definition of Basic and Supplementary Unit of S.I. 
1. Metre (m): The metre is the length of the path travelled by light in vacuum during a time 
interval of 1/299 792 458 of a second. 
2. Kilogram (Kg) : The kilogram is the mass of the platinum-iridium prototype which was 
 approved by the ConférenceGénérale des Poids et Mesures, held in Paris in  1889, and kept 
by the Bureau International des Poids et Mesures. 
3. Second (s): The second is the duration of 9192631770 periods of the radiation 
corresponding to the transition between two hyperfine levels of the ground state of Cesium-
133 atom. 
4. Ampere (A) : The ampere is the intensity of a constant current which, if maintained in two 
straight  parallel conductors of infinite length, of negligible circular cross-section, and  placed 
1 metre apart in vacuum, would produce between these conductors a  force equal to 2 ? 10
-
7
Newton per metre of length. 
5. Kelvin (K): Kelvin is the fraction 1/273.16 of the thermodynamic temperature of the triple 
point of water. 
6. Candela (Cd): The candela is the luminous intensity, in a given direction, of a source that 
emits monochromatic radiation of frequency 540 x 10
12
 hertz and that has a radiant intensity 
in that direction of 1/683 watt per steradian. 
7. Mole (mol): The mole is the amount of substance of a system which contains as many 
elementary entities as there are atoms in 0.012 kilogram of Carbon-12. 
Supplementary units: 
1. Radian (rad): It is supplementary unit of plane angle. It is the plane angle subtended 
at the centre of a circle by an arc of the circle equal to the radius of the circle. It is 
denoted by ?? . 
   ?? = l / r;  ?? is length of the arcand ?? is radius of the circle 
2. Steradian (Sr): It is supplementary unit of solid angle. It is the angle subtended at the 
centre of a sphere by a surface area of the sphere having magnitude equal to the 
square of the radius of the sphere. It is denoted by ?. 
? = ?s / r
2
 
SOME IMPORTANT ABBREVIATIONS 
Symbol Prefix Multiplier Symbol Prefix Multiplier 
D 
c 
m 
µ 
n 
Deci 
centi 
milli 
micro 
nano 
10
-1
 
10
-2
 
10
-3
 
10
-6
 
10
-9
 
da 
h 
k 
M 
G 
deca 
hecto 
kilo 
mega 
giga 
10
1
 
10
2
 
10
3
 
10
6
 
10
9
 
5 
 
P 
f 
a 
 
Pico 
femto 
atto 
10
-12
 
10
-15
 
10
-18
 
 
T 
P 
E 
tera 
Pecta 
exa 
 
10
12
 
10
15
 
10
18
 
 
 
Some Important Units of Length: 
(i) 1 micron = 10
–6
 m = 10
–4
 cm 
(ii) 1 angstrom = 1Å = 10
–10
 m = 10
–8
 cm  
(iii) 1 fermi = 1 fm = 10
–15
 m 
(iv) 1 Light year = 1 ly = 9.46 x 10
15
m 
(v) 1 Parsec = 1pc = 3.26 light year 
Some conversion factor of mass: 
1 Kilogram = 2.2046 pound 
1 Pound = 453.6 gram 
1 kilogram = 1000 gram 
1 milligram = 1/1000 gram = 10
-3
 gram 
1 centigram = 1/100 gram = 10
-2
 gram 
1 decigram = 1/10 gram 
1 quintal = 100 kg 
1 metric ton = 1000 kilogram 
1.4  DEFINITION OF DIMENSIONS 
Dimensions: The powers, to which the fundamental units of mass, length and time 
written as M, L and T are raised, which include their nature and not their magnitude. 
For example  Area = Length x Breadth 
    = [ L
1
] × [L
1
] = [L
2
] = [M
0
L
2
T
0
] 
Power (0,2,0) of fundamental units are called dimensions of area in mass, length and time 
respectively. 
e.g.      Density = mass/volume  
   = [M]/[L
3
] 
   = [ M
1
L
-3
T
0
] 
 
1.5  DIMENSIONAL FORMULAE AND SI UNITS OF PHYSICAL QUANTITIES