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Units & Measurement Class 11 Notes Physics Chapter 1

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 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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FAQs on Units & Measurement Class 11 Notes Physics Chapter 1

1. What are the different dimensions used in measurements?
Ans. Dimensions used in measurements include length, width, height, time, temperature, mass, volume, and many others. These dimensions help quantify objects and phenomena in various fields such as science, engineering, and everyday life.
2. How do you measure length accurately?
Ans. To measure length accurately, you can use a ruler, tape measure, or calipers. Ensure that the object being measured is aligned properly with the measuring tool, and read the measurement by aligning your eyes with the scale. For even more precise measurements, consider using digital measuring tools.
3. What is the importance of accurate measurements in scientific experiments?
Ans. Accurate measurements are crucial in scientific experiments as they help ensure reliable and valid results. Precise measurements enable scientists to make accurate observations, collect data, and analyze experimental outcomes. This accuracy allows for the replication of experiments and the formulation of scientific laws and theories.
4. How do you convert between different units of measurement?
Ans. To convert between different units of measurement, you can use conversion factors. A conversion factor is a ratio that relates two different units of the same dimension. Multiply the original measurement by the appropriate conversion factor to obtain the desired unit. For example, to convert meters to centimeters, multiply the measurement by 100.
5. What is the significance of standard units of measurement?
Ans. Standard units of measurement provide a consistent and universally accepted framework for measuring and comparing quantities. They enable accurate communication of measurements across different regions and disciplines. Standard units, such as the International System of Units (SI), facilitate scientific research, international trade, and technological advancements.
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