Page 1
1
A quantity which can be measured and expressed in form of laws is called
a physical quantity. Physical quantity (Q) = Magnitude × Unit = n × u
Where, n represents the numerical value and u represents the unit. as
the unit(u) changes, the magnitude (n) will also change but product ‘nu’
will remain same.
i.e. n u = constant, or n
1
u
1
= n
2
u
2
= constant;
Any unit of mass, length and time in mechanics is called a fundamental,
absolute or base unit. Other units which can be expressed in terms of
fundamental units, are called derived units
System of units : A complete set of units, both fundamental and derived
for all kinds of physical quantities is called system of units.
(1) CGS system, (2) MKS system, (3) FPS system.
(4) S.I. system : It is known as International system of units. There are
seven fundamental quantities in this system. These quantities and their
units are given in the following table.
Quantity Name of Units 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
Page 2
1
A quantity which can be measured and expressed in form of laws is called
a physical quantity. Physical quantity (Q) = Magnitude × Unit = n × u
Where, n represents the numerical value and u represents the unit. as
the unit(u) changes, the magnitude (n) will also change but product ‘nu’
will remain same.
i.e. n u = constant, or n
1
u
1
= n
2
u
2
= constant;
Any unit of mass, length and time in mechanics is called a fundamental,
absolute or base unit. Other units which can be expressed in terms of
fundamental units, are called derived units
System of units : A complete set of units, both fundamental and derived
for all kinds of physical quantities is called system of units.
(1) CGS system, (2) MKS system, (3) FPS system.
(4) S.I. system : It is known as International system of units. There are
seven fundamental quantities in this system. These quantities and their
units are given in the following table.
Quantity Name of Units 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
Besides the above seven fundamental units two supplementary units are
also defined - Radian ( rad) for plane angle and Steradian (sr) for solid
angle.
1.3 Dimensions of a Physical Quantity
When a derived quantity is expressed in terms of fundamental quantities,
it is written as a product of different powers of the fundamental quantities.
The powers to which fundamental quantities must be raised in order to
express the given physical quantity are called its dimensions.
1.4 Important Dimensions of Complete Physics
Mechanics
S.N. Quantity Unit Dimension
(1) Velocity or speed (v) m/s [M
0
L
1
T
–1
]
(2) Acceleration (a) m/s
2
[M
0
LT
–2
]
(3) Momentum (P) kg.m/s [M
1
L
1
T
–1
]
(4) Impulse (I) Newton sec or [M
1
L
1
T
–1
]
kg. m/s
(5) Force (F) Newton [M
1
L
1
T
–2
]
(6) Pressure (P) Pascal [M
1
L
–1
T
–2
]
(7) Kinetic energy (E
k
) Joule [M
1
L
2
T
–2
]
(8) Power (P) Watt or Joule/s [M
1
L
2
T
–3
]
(9) Density (d) kg/m
3
[M
1
L
–3
T
0
]
(10) Angular displacement ( ? ) Radian (rad.) [M
0
L
0
T
0
]
(11) Angular velocity ( ? ) Radian/sec [M
0
L
0
T
–1
]
(12) Angular Acceleratio n ( a ) Radian/sec
2
[M
0
L
0
T
–2
]
(13) Moment of inertia (I) kg.m
2
[ML
2
T
0
]
(14) T orque ( t ) Newton-meter [ML
2
T
-2
]
(15) Angular momentum (L) Joule sec [ML
2
T
–1
]
(16) Force constant or spring constant (k) Newton/m [M
1
L
0
T
–2
]
(17) Gravitational constant (G) N–m
2
/kg
2
[M
–1
L
3
T
–2
]
Page 3
1
A quantity which can be measured and expressed in form of laws is called
a physical quantity. Physical quantity (Q) = Magnitude × Unit = n × u
Where, n represents the numerical value and u represents the unit. as
the unit(u) changes, the magnitude (n) will also change but product ‘nu’
will remain same.
i.e. n u = constant, or n
1
u
1
= n
2
u
2
= constant;
Any unit of mass, length and time in mechanics is called a fundamental,
absolute or base unit. Other units which can be expressed in terms of
fundamental units, are called derived units
System of units : A complete set of units, both fundamental and derived
for all kinds of physical quantities is called system of units.
(1) CGS system, (2) MKS system, (3) FPS system.
(4) S.I. system : It is known as International system of units. There are
seven fundamental quantities in this system. These quantities and their
units are given in the following table.
Quantity Name of Units 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
Besides the above seven fundamental units two supplementary units are
also defined - Radian ( rad) for plane angle and Steradian (sr) for solid
angle.
1.3 Dimensions of a Physical Quantity
When a derived quantity is expressed in terms of fundamental quantities,
it is written as a product of different powers of the fundamental quantities.
The powers to which fundamental quantities must be raised in order to
express the given physical quantity are called its dimensions.
1.4 Important Dimensions of Complete Physics
Mechanics
S.N. Quantity Unit Dimension
(1) Velocity or speed (v) m/s [M
0
L
1
T
–1
]
(2) Acceleration (a) m/s
2
[M
0
LT
–2
]
(3) Momentum (P) kg.m/s [M
1
L
1
T
–1
]
(4) Impulse (I) Newton sec or [M
1
L
1
T
–1
]
kg. m/s
(5) Force (F) Newton [M
1
L
1
T
–2
]
(6) Pressure (P) Pascal [M
1
L
–1
T
–2
]
(7) Kinetic energy (E
k
) Joule [M
1
L
2
T
–2
]
(8) Power (P) Watt or Joule/s [M
1
L
2
T
–3
]
(9) Density (d) kg/m
3
[M
1
L
–3
T
0
]
(10) Angular displacement ( ? ) Radian (rad.) [M
0
L
0
T
0
]
(11) Angular velocity ( ? ) Radian/sec [M
0
L
0
T
–1
]
(12) Angular Acceleratio n ( a ) Radian/sec
2
[M
0
L
0
T
–2
]
(13) Moment of inertia (I) kg.m
2
[ML
2
T
0
]
(14) T orque ( t ) Newton-meter [ML
2
T
-2
]
(15) Angular momentum (L) Joule sec [ML
2
T
–1
]
(16) Force constant or spring constant (k) Newton/m [M
1
L
0
T
–2
]
(17) Gravitational constant (G) N–m
2
/kg
2
[M
–1
L
3
T
–2
]
(18) Intensity of gravitational field (E
g
) N/kg [M
0
L
1
T
–2
]
(19) Gravitational potential (V
g
) Joule/kg [M
0
L
2
T
–2
]
(20) Surface tension (T) N/m or Joule/m
2
[M
1
L
0
T
–2
]
(21) Velocity gradient (V
g
) Second
–1
[M
0
L
0
T
–1
]
(22) Coefficient of viscosity ( ?) kg/m s [M
1
L
–1
T
–1
]
(23) Stress N/m
2
[M
1
L
–1
T
–2
]
(24) Strain No unit [M
0
L
0
T
0
]
(25) Modulus of elasticity (E) N/m
2
[M
0
L
–1
T
–2
]
(26) Poisson Ratio ( s) No unit [M
0
L
0
T
0
]
(27) Time period (T) Second [M
0
L
0
T
1
]
(28) Frequency ( n ) Hz [M
0
L
0
T
–1
]
Heat
S.N. Quantity Unit Dimension
(1) Temperature (T) Kelvin M
0
L
0
T
0
K
1
]
(2) Heat (Q) Joule [ML
2
T
–2
]
(3) Specific Heat ( c) Joule/Kg–K [M
0
L
2
T
–2
K
–1
]
(4) Thermal capacity Joule/K [M
1
L
2
T
–2
K
–1
]
(5) Latent heat (L) Joule/kg [M
0
L
2
T
–2
]
(6) Gas constant (R) Joule/mol-K [M
1
L
2
T
–2
mol
–1
K
–1
]
(7) Boltzmann constant (k) Joule/K [M
1
L
2
T
–2
K
–1
]
(8) Coefficient of thermal Joule/M-s-K [M
1
L
1
T
–3
K
–1
]
conductivity (K)
(9) Stefan’s constant ( s) Watt/m
2
–K
4
[M
1
L
0
T
–3
K
–4
]
(10) Wien’s constant (b) Meter K [M
0
L
1
T
0
K
1
]
(11) Planck’s constant (h) Joule s [M
1
L
2
T
–1
]
(12) Coefficient of Linear K e l v i n
–1
[M
0
L
0
T
0
K
–1
]
Expansion
Page 4
1
A quantity which can be measured and expressed in form of laws is called
a physical quantity. Physical quantity (Q) = Magnitude × Unit = n × u
Where, n represents the numerical value and u represents the unit. as
the unit(u) changes, the magnitude (n) will also change but product ‘nu’
will remain same.
i.e. n u = constant, or n
1
u
1
= n
2
u
2
= constant;
Any unit of mass, length and time in mechanics is called a fundamental,
absolute or base unit. Other units which can be expressed in terms of
fundamental units, are called derived units
System of units : A complete set of units, both fundamental and derived
for all kinds of physical quantities is called system of units.
(1) CGS system, (2) MKS system, (3) FPS system.
(4) S.I. system : It is known as International system of units. There are
seven fundamental quantities in this system. These quantities and their
units are given in the following table.
Quantity Name of Units 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
Besides the above seven fundamental units two supplementary units are
also defined - Radian ( rad) for plane angle and Steradian (sr) for solid
angle.
1.3 Dimensions of a Physical Quantity
When a derived quantity is expressed in terms of fundamental quantities,
it is written as a product of different powers of the fundamental quantities.
The powers to which fundamental quantities must be raised in order to
express the given physical quantity are called its dimensions.
1.4 Important Dimensions of Complete Physics
Mechanics
S.N. Quantity Unit Dimension
(1) Velocity or speed (v) m/s [M
0
L
1
T
–1
]
(2) Acceleration (a) m/s
2
[M
0
LT
–2
]
(3) Momentum (P) kg.m/s [M
1
L
1
T
–1
]
(4) Impulse (I) Newton sec or [M
1
L
1
T
–1
]
kg. m/s
(5) Force (F) Newton [M
1
L
1
T
–2
]
(6) Pressure (P) Pascal [M
1
L
–1
T
–2
]
(7) Kinetic energy (E
k
) Joule [M
1
L
2
T
–2
]
(8) Power (P) Watt or Joule/s [M
1
L
2
T
–3
]
(9) Density (d) kg/m
3
[M
1
L
–3
T
0
]
(10) Angular displacement ( ? ) Radian (rad.) [M
0
L
0
T
0
]
(11) Angular velocity ( ? ) Radian/sec [M
0
L
0
T
–1
]
(12) Angular Acceleratio n ( a ) Radian/sec
2
[M
0
L
0
T
–2
]
(13) Moment of inertia (I) kg.m
2
[ML
2
T
0
]
(14) T orque ( t ) Newton-meter [ML
2
T
-2
]
(15) Angular momentum (L) Joule sec [ML
2
T
–1
]
(16) Force constant or spring constant (k) Newton/m [M
1
L
0
T
–2
]
(17) Gravitational constant (G) N–m
2
/kg
2
[M
–1
L
3
T
–2
]
(18) Intensity of gravitational field (E
g
) N/kg [M
0
L
1
T
–2
]
(19) Gravitational potential (V
g
) Joule/kg [M
0
L
2
T
–2
]
(20) Surface tension (T) N/m or Joule/m
2
[M
1
L
0
T
–2
]
(21) Velocity gradient (V
g
) Second
–1
[M
0
L
0
T
–1
]
(22) Coefficient of viscosity ( ?) kg/m s [M
1
L
–1
T
–1
]
(23) Stress N/m
2
[M
1
L
–1
T
–2
]
(24) Strain No unit [M
0
L
0
T
0
]
(25) Modulus of elasticity (E) N/m
2
[M
0
L
–1
T
–2
]
(26) Poisson Ratio ( s) No unit [M
0
L
0
T
0
]
(27) Time period (T) Second [M
0
L
0
T
1
]
(28) Frequency ( n ) Hz [M
0
L
0
T
–1
]
Heat
S.N. Quantity Unit Dimension
(1) Temperature (T) Kelvin M
0
L
0
T
0
K
1
]
(2) Heat (Q) Joule [ML
2
T
–2
]
(3) Specific Heat ( c) Joule/Kg–K [M
0
L
2
T
–2
K
–1
]
(4) Thermal capacity Joule/K [M
1
L
2
T
–2
K
–1
]
(5) Latent heat (L) Joule/kg [M
0
L
2
T
–2
]
(6) Gas constant (R) Joule/mol-K [M
1
L
2
T
–2
mol
–1
K
–1
]
(7) Boltzmann constant (k) Joule/K [M
1
L
2
T
–2
K
–1
]
(8) Coefficient of thermal Joule/M-s-K [M
1
L
1
T
–3
K
–1
]
conductivity (K)
(9) Stefan’s constant ( s) Watt/m
2
–K
4
[M
1
L
0
T
–3
K
–4
]
(10) Wien’s constant (b) Meter K [M
0
L
1
T
0
K
1
]
(11) Planck’s constant (h) Joule s [M
1
L
2
T
–1
]
(12) Coefficient of Linear K e l v i n
–1
[M
0
L
0
T
0
K
–1
]
Expansion
(13) Mechanical eq. of Heat (J) Joule/Calorie [M
0
L
0
T
0
]
(14) Vander wall’s constant (a) Newton m
4
[M
1
L
5
T
–2
]
(15) Vander wall’s consatnt (b) m
3
[M
0
L
3
T
0
]
1.5 Quantities Having Same Dimensions
S.N. Dimension Quantity
(1) [M
0
L
0
T
–1
] Frequency, angular frequency, angular velocity, velocity
gradient and decay constant
(2) [M
1
L
2
T
–2
] Work, internal energy, potential energy, kinetic energy,
torque, moment of force
(3) [M
1
L
–1
T
–2
] Pressure, stress, Y oung’s modulus, bulk modulus, modulus
of rigidity, energy density
(4) [M
1
L
1
T
–1
] Momentum, impulse
(5) [M
0
L
1
T
–2
] Acceleration due to gravity , gravitational field intensity
(6) [M
1
L
1
T
–2
] Thrust, force, weight, energy gradient
(7) [M
1
L
2
T
–1
] Angular momentum and Planck’s constant
(8) [M
1
L
0
T
–2
] Surface tension, Surface energy (energy per unit area)
(9) [M
0
L
0
T
0
] Strain, refractive index, relative density, angle, solid
angle, distance gradient, relative permittivity (dielectric
constant), relative permeability etc.
(10) [M
0
L
2
T
–2
] Latent heat and gravitational potential
(1 1) [M
0
L
0
T
–2
K
–1
] Thermal capacity, gas constant, Boltzmann constant and
entropy
(12) [M
0
L
0
T
1
]
g = acceleration due to gravity, m = mass, k = spring
constant
(13) [M
0
L
0
T
1
] L/R RC where L = inductance, R = resistance,
C = capacitance
(14) [ML
2
T
–2
] I
2
Rt, Vlt, qV, Ll
2
, CV
2
where I = current,
t = time q = charge, L = inductance, C = capacitance,
R = resistanc e
Page 5
1
A quantity which can be measured and expressed in form of laws is called
a physical quantity. Physical quantity (Q) = Magnitude × Unit = n × u
Where, n represents the numerical value and u represents the unit. as
the unit(u) changes, the magnitude (n) will also change but product ‘nu’
will remain same.
i.e. n u = constant, or n
1
u
1
= n
2
u
2
= constant;
Any unit of mass, length and time in mechanics is called a fundamental,
absolute or base unit. Other units which can be expressed in terms of
fundamental units, are called derived units
System of units : A complete set of units, both fundamental and derived
for all kinds of physical quantities is called system of units.
(1) CGS system, (2) MKS system, (3) FPS system.
(4) S.I. system : It is known as International system of units. There are
seven fundamental quantities in this system. These quantities and their
units are given in the following table.
Quantity Name of Units 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
Besides the above seven fundamental units two supplementary units are
also defined - Radian ( rad) for plane angle and Steradian (sr) for solid
angle.
1.3 Dimensions of a Physical Quantity
When a derived quantity is expressed in terms of fundamental quantities,
it is written as a product of different powers of the fundamental quantities.
The powers to which fundamental quantities must be raised in order to
express the given physical quantity are called its dimensions.
1.4 Important Dimensions of Complete Physics
Mechanics
S.N. Quantity Unit Dimension
(1) Velocity or speed (v) m/s [M
0
L
1
T
–1
]
(2) Acceleration (a) m/s
2
[M
0
LT
–2
]
(3) Momentum (P) kg.m/s [M
1
L
1
T
–1
]
(4) Impulse (I) Newton sec or [M
1
L
1
T
–1
]
kg. m/s
(5) Force (F) Newton [M
1
L
1
T
–2
]
(6) Pressure (P) Pascal [M
1
L
–1
T
–2
]
(7) Kinetic energy (E
k
) Joule [M
1
L
2
T
–2
]
(8) Power (P) Watt or Joule/s [M
1
L
2
T
–3
]
(9) Density (d) kg/m
3
[M
1
L
–3
T
0
]
(10) Angular displacement ( ? ) Radian (rad.) [M
0
L
0
T
0
]
(11) Angular velocity ( ? ) Radian/sec [M
0
L
0
T
–1
]
(12) Angular Acceleratio n ( a ) Radian/sec
2
[M
0
L
0
T
–2
]
(13) Moment of inertia (I) kg.m
2
[ML
2
T
0
]
(14) T orque ( t ) Newton-meter [ML
2
T
-2
]
(15) Angular momentum (L) Joule sec [ML
2
T
–1
]
(16) Force constant or spring constant (k) Newton/m [M
1
L
0
T
–2
]
(17) Gravitational constant (G) N–m
2
/kg
2
[M
–1
L
3
T
–2
]
(18) Intensity of gravitational field (E
g
) N/kg [M
0
L
1
T
–2
]
(19) Gravitational potential (V
g
) Joule/kg [M
0
L
2
T
–2
]
(20) Surface tension (T) N/m or Joule/m
2
[M
1
L
0
T
–2
]
(21) Velocity gradient (V
g
) Second
–1
[M
0
L
0
T
–1
]
(22) Coefficient of viscosity ( ?) kg/m s [M
1
L
–1
T
–1
]
(23) Stress N/m
2
[M
1
L
–1
T
–2
]
(24) Strain No unit [M
0
L
0
T
0
]
(25) Modulus of elasticity (E) N/m
2
[M
0
L
–1
T
–2
]
(26) Poisson Ratio ( s) No unit [M
0
L
0
T
0
]
(27) Time period (T) Second [M
0
L
0
T
1
]
(28) Frequency ( n ) Hz [M
0
L
0
T
–1
]
Heat
S.N. Quantity Unit Dimension
(1) Temperature (T) Kelvin M
0
L
0
T
0
K
1
]
(2) Heat (Q) Joule [ML
2
T
–2
]
(3) Specific Heat ( c) Joule/Kg–K [M
0
L
2
T
–2
K
–1
]
(4) Thermal capacity Joule/K [M
1
L
2
T
–2
K
–1
]
(5) Latent heat (L) Joule/kg [M
0
L
2
T
–2
]
(6) Gas constant (R) Joule/mol-K [M
1
L
2
T
–2
mol
–1
K
–1
]
(7) Boltzmann constant (k) Joule/K [M
1
L
2
T
–2
K
–1
]
(8) Coefficient of thermal Joule/M-s-K [M
1
L
1
T
–3
K
–1
]
conductivity (K)
(9) Stefan’s constant ( s) Watt/m
2
–K
4
[M
1
L
0
T
–3
K
–4
]
(10) Wien’s constant (b) Meter K [M
0
L
1
T
0
K
1
]
(11) Planck’s constant (h) Joule s [M
1
L
2
T
–1
]
(12) Coefficient of Linear K e l v i n
–1
[M
0
L
0
T
0
K
–1
]
Expansion
(13) Mechanical eq. of Heat (J) Joule/Calorie [M
0
L
0
T
0
]
(14) Vander wall’s constant (a) Newton m
4
[M
1
L
5
T
–2
]
(15) Vander wall’s consatnt (b) m
3
[M
0
L
3
T
0
]
1.5 Quantities Having Same Dimensions
S.N. Dimension Quantity
(1) [M
0
L
0
T
–1
] Frequency, angular frequency, angular velocity, velocity
gradient and decay constant
(2) [M
1
L
2
T
–2
] Work, internal energy, potential energy, kinetic energy,
torque, moment of force
(3) [M
1
L
–1
T
–2
] Pressure, stress, Y oung’s modulus, bulk modulus, modulus
of rigidity, energy density
(4) [M
1
L
1
T
–1
] Momentum, impulse
(5) [M
0
L
1
T
–2
] Acceleration due to gravity , gravitational field intensity
(6) [M
1
L
1
T
–2
] Thrust, force, weight, energy gradient
(7) [M
1
L
2
T
–1
] Angular momentum and Planck’s constant
(8) [M
1
L
0
T
–2
] Surface tension, Surface energy (energy per unit area)
(9) [M
0
L
0
T
0
] Strain, refractive index, relative density, angle, solid
angle, distance gradient, relative permittivity (dielectric
constant), relative permeability etc.
(10) [M
0
L
2
T
–2
] Latent heat and gravitational potential
(1 1) [M
0
L
0
T
–2
K
–1
] Thermal capacity, gas constant, Boltzmann constant and
entropy
(12) [M
0
L
0
T
1
]
g = acceleration due to gravity, m = mass, k = spring
constant
(13) [M
0
L
0
T
1
] L/R RC where L = inductance, R = resistance,
C = capacitance
(14) [ML
2
T
–2
] I
2
Rt, Vlt, qV, Ll
2
, CV
2
where I = current,
t = time q = charge, L = inductance, C = capacitance,
R = resistanc e
1.6 Application of Dimensional Analysis.
(1) T o find the unit of a physical quantity in a given system of units.
(2) T o find dimensions of physical constant or coefficients.
(3) To convert a physical quantity from one system to the other.
(4) To check the dimensional correctness of a given physical relation: This is
based on the ‘principle of homogeneity’. According to this principle the
dimensions of each term on both sides of an equation must be the same.
(5) To derive new relations.
1.7 Limitations of Dimensional Analysis.
(1) If dimensions are given, physical quantity may not be unique.
(2) Numerical constant having no dimensions cannot be deduced by the methods
of dimensions.
(3) The method of dimensions can not be used to derive relations other than
product of power functions. For example,
s = u t + (1/2) at
2
or y = a sin ? t
(4) The method of dimensions cannot be applied to derive formula consist of
more than 3 physical quantities.
1.8 Significant Figures
Significant figures in the measured value of a physical quantity tell the
number of digits in which we have confidence. Lar ger the number of
significant figures obtained in a measurement, greater is the accuracy of
the measurement. The reverse is also true.
The following rules are observed in counting the number of significant
figures in a given measured quantity .
(1) All non-zero digits are significant.
(2) A zero becomes significant figure if it appears between two non-zero digits.
(3) Leading zeros or the zeros placed to the left of the number are never
significant.
Example : 0.543 has three significant figures.
0.006 has one significant figures.
(4) T railing zeros or the zeros placed to the right of the number are significant.
Example : 4.330 has four significant figures.
343.000 has six significant figures.
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