EB
8 PHYSICS
Units and
2 Measurements
PHYSICAL QUANTITY Fundamental (or Base) and Derived Units
All the quantities in terms of which laws of physics are described Fundamental units are those, which are independent of unit of
and which can be measured directly or indirectly are called other physical quantity and cannot be further resolved into any
physical quantities. For example mass, length, time, speed, force other units or the units of fundamental physical quantities are
etc. called fundamental or base units. e.g., kilogram, metre, second
Types of Physical Quantity etc,
1. Fundamental quantities : The physical quantities which do All units other than fundamental are derived units (which are
not depend upon other physical quantities are called dependent on fundamental units) e.g., unit of speed (ms–1) which
fundamental or base physical quantities. e.g. mass, length, depends on unit of length (metre) and unit of time (second), unit
time temperature electric current, luminous intensity and of momentum (Kgms–1) depends on unit of mass, length and time
amount of substance. etc.
2. Derived quantities :The physical quantities which depend SYSTEM OF UNITS
on fundamental quantities are called derived quantities A system of units is a complete set of fundamental and derived
e.g. speed, acceleration, force, etc. units for all physical quantities.
UNIT Different types of system of units
The process of measurement is a comparison process. F.P.S. (Foot - Pound - Second) system. (British engineering system
Unit is the standard quantity used for comparision. of units.): In this system the unit of length is foot, mass is pound
The chosen standard for measurement of a physical quantity, and time is second.
which has the same nature as that of the quantity is called the C.G.S. (Centimetre - Gram - Second) system. (Gaussian system
unit of that quantity. of units): In this system the unit of length is centimetre, mass is
Choice of a unit (Characteristics of a unit): gram and time is second.
(1) It should be suitable in size (suitable to use) M.K.S (Metre - Kilogram - Second) system. This system is related
(2) It should be accurately defined (so that everybody to mechanics only. In this system the unit of length is metre, mass
understands the unit in same way) is kilogram and time is second.
(3) It should be easily reproducible. S.I. (International system) units: (Introduced in 1971) Different
(4) It should not change with time. countries use different set of units. To avoid complexity, by
(5) It should not change with change in physical conditions international agreement, seven physical quantities have been
i.e., temperature, pressure, moisture etc. chosen as fundamental or base physical quantities and two as
(6) It should be universally acceptable. supplementary. These quantities are
Every measured quantity (its magnitude) comprises of a number
and a unit. Ex: In the measurement of time, say S.No Base physical quantity Fundamental unit Symbol
15 s 1 Mass kilogram kg
Number (n) Unit (u) 2 Length metre m
If Q is the magnitude of the quantity (which does not depend on 3 Time second s
the selection of unit) then
4 Temperature kelvin K
1
Q = n u = n1 u1 = n2 u2 Þ n µ 5 Electric current ampere A
u
6 Luminous intensity candela cd
Where u1 and u2 are the units and n1 and n2 are the numerical
values in two different system of units. 7 Amount of substance mole mol
, Units and Measurements 9
S.No Supplementary physical Supplementary unit Symbol Prefix Power of 10 Symbol
quantity exa 18 E
1 Plane angle radian rad
peta 15 P
tera 12 T
2 Solid angle steradian sr
giga 9 G
Merits of S.I. Units : mega 6 M
(1) SI is a coherent system of units: This means that all derived kilo 3 k
units are obtained by multiplication and division without hecto 2 h
introducing any numerical factor.
deca 1 da
(2) SI is a rational system of units: This is because it assigns
deci –1 d
only one unit to a particular physical quantity.
centi –2 c
(3) SI is an absolute system of units: There is no gravitational
unit in this system. milli –3 m
micro –6 m
(4) SI system is applicable to all branches of science.
nano –9 n
Conventions of writing of Units and their Symbols pico –12 p
· Unit is never written with capital initial letter.
femto –15 f
· For a unit named after scientist the symbol is a capital
letter otherwise not. atto –18 a
· The unit or symbol is never written in plural form. Some Important Practical Units :
· Punctuations marks are not written after the symbol. (1) For large distance (macro-cosm)
Definitions of Fundamental Units (a) Astronomical unit: It is the average distance of the
(i) Metre : One metre is equal to 1650763.73 wavelength in centre of the sun from the centre of the earth.
vacuum of the radiation corresponding to transition between 1 A.U. = 1.496 × 1011m
the levels 2p10 and 5d5 of the krypton – 86 atom (b) Light year: It is the distance travelled by the light in
Or vacuum in one year. 1 ly = 9.46 × 1015m
The distance travelled by light in vacuum in (c) Parsec: One parsec is the distance at which an arc
1A.U. long subtends an angle of one second.
1 1 parsec = 3.1 × 1016m
second is called 1 metre.
299,792, 458 (2) For small distance (micro-cosm)
(ii) Kilogram : The mass of cylinder (of height and diameter 1 micron = 10–6m 1nanometre = 10–9m
1angstorm = 10 m –10 1fermi = 10–15m
39 cm) made of Platinum-iridium alloy kept at International
Bureau of weights and measures in paris is defined as 1kg. (3) For small area 1 barn = 10–28m2
(iii) Second : It is the duration of 9,192,631,770 periods of (4) For heavy mass 1 ton = 1000kg
radiation corresponding to the transition between the two 1quintal = 100kg 1slug = 14.57kg
hyperfine levels of the ground state of Caesium (133) atom. 1 C.S.L (chandrasekhar limit) = 1.4 times the mass of the sun
(5) For small mass 1 amu = 1.67 x 10–27kg
(iv) Ampere : It is the current which when flows through two
1 pound = 453.6g = 0.4536 kg
infinitely long straight conductors of negligible cross-
(6) For small time 1 shake = 10–8s
section placed at a distance of one metre in air or vacuum
(7) For large time
produces a force of 2 × 10–7 N/m between them.
Lunar month: It is the time taken by the earth to complete
(v) Candela : It is the luminous intensity in a perpendicular one rotation about its axis with respect to sun.
direction, of a surface of 1/600,000 square metre of a black 1L.M. = 27.3 days.
body at the temperature of freezing platinum under a pressure Solar day: It is the time taken by the earth to complete one
of 1.013 × 105 N/m2. rotation about its axis with respect to sun.
(vi) Kelvin : It is the 1/273.16 part of thermodynamic temperature Sedrial day: It is the time taken by earth to complete one
of triple point of water. rotation on its axis with respect to distant star.
(vii) Mole : It is the amount of substance which contains as many (8) For measuring pressure
elementary entities as there are in 0.012 kg of Carbon-12. 1 bar = 1atm pressure = 105N/m2 = 760mmHg
S.I. Prefixes : 1torr = 1 mmHg
The magnitudes of physical quantities vary over a wide range. 1 poiseuille = 10 Poise.
For example, the atomic radius, is equal to 10 –10m, radius of earth DIMENSIONS
is 6.4×106 m and the mass of electron is 9.1×10–31 kg. The The powers to which the fundamental units of mass, length and
internationally recommended standard prefixes for certain powers time must be raised to represent the physical quantity are called
of 10 are given in the table: the dimensions of that physical quantity.
, EB
10 PHYSICS
For example : Force = mass × acceleration called dimensional formula. It shows how and which of the
fundamental quantities represent the dimensions.
v–u [LT -1]
= mass × = [M] T–2]
= [MLT For example, the dimensional formula of work is [ML2T–2]
t [T]
Hence the dimensions of force are 1 in mass 1 in length and (– 2) Dimensional Equation :
in time. When we equate the dimensional formula with the physical
Dimensional Formula : quantity, we get the dimensional equation.
Unit of a physical quantity expressed in terms of M, L and T is For example Work = [ML2T–2]
Classification of Physical Quantities (On the basis of dimensions) :
Dimensional Dimensional For e.g. c (velocity of light in vaccum)
physical quantity constant R(universal gas constant),
s(stefan's constant), h (Planck's constant),
k (Boltzmann constant), G (universal gravitational constant) etc.
Physical Dimensional For e.g. distance, displacement, force, mass, time etc.
Quantity variable
Dimensionless Dimensionless For e.g. 0, 1, 2, ....., e, p , sin q , cos q , tan q , etc.
physical quantity constant
Dimensionless For e.g. plane angle, solid angle, strain,
variable refractive index, dielectric constant, relative density,
specific gravity, poisson's ratio etc.
Dimensional Formula of Some Important Physical Quantities :
S.No. Physical quantity Relation with other quantities Dimensional formula
Length
1. Velocity (v) [M0LT–1]
Time
Velocity
2. Acceleration (a) [M0LT–2]
Time
3. Momentum (p) Mass × velocity [MLT–1]
4. Force (F) Mass × acceleration [MLT–2]
5. Work Force × displacement [ML2T–2]
6. Power (P) Work [ML2T–3]
Time
Fr 2
7. Universal gravitational constant G= [M–1L3T–2 ]
m1m 2
8. Torque t = r ´F [ML2T–2]
F
9. Surface tension S= [MT–2]
l
W
10. Gravitational potential VG = [M0L2T–2]
m
F
11. Coefficient of viscosity h= [ML–1T–1]
dv
A
dx
12. Impulse Force×time(F×t) [MLT–1]
8 PHYSICS
Units and
2 Measurements
PHYSICAL QUANTITY Fundamental (or Base) and Derived Units
All the quantities in terms of which laws of physics are described Fundamental units are those, which are independent of unit of
and which can be measured directly or indirectly are called other physical quantity and cannot be further resolved into any
physical quantities. For example mass, length, time, speed, force other units or the units of fundamental physical quantities are
etc. called fundamental or base units. e.g., kilogram, metre, second
Types of Physical Quantity etc,
1. Fundamental quantities : The physical quantities which do All units other than fundamental are derived units (which are
not depend upon other physical quantities are called dependent on fundamental units) e.g., unit of speed (ms–1) which
fundamental or base physical quantities. e.g. mass, length, depends on unit of length (metre) and unit of time (second), unit
time temperature electric current, luminous intensity and of momentum (Kgms–1) depends on unit of mass, length and time
amount of substance. etc.
2. Derived quantities :The physical quantities which depend SYSTEM OF UNITS
on fundamental quantities are called derived quantities A system of units is a complete set of fundamental and derived
e.g. speed, acceleration, force, etc. units for all physical quantities.
UNIT Different types of system of units
The process of measurement is a comparison process. F.P.S. (Foot - Pound - Second) system. (British engineering system
Unit is the standard quantity used for comparision. of units.): In this system the unit of length is foot, mass is pound
The chosen standard for measurement of a physical quantity, and time is second.
which has the same nature as that of the quantity is called the C.G.S. (Centimetre - Gram - Second) system. (Gaussian system
unit of that quantity. of units): In this system the unit of length is centimetre, mass is
Choice of a unit (Characteristics of a unit): gram and time is second.
(1) It should be suitable in size (suitable to use) M.K.S (Metre - Kilogram - Second) system. This system is related
(2) It should be accurately defined (so that everybody to mechanics only. In this system the unit of length is metre, mass
understands the unit in same way) is kilogram and time is second.
(3) It should be easily reproducible. S.I. (International system) units: (Introduced in 1971) Different
(4) It should not change with time. countries use different set of units. To avoid complexity, by
(5) It should not change with change in physical conditions international agreement, seven physical quantities have been
i.e., temperature, pressure, moisture etc. chosen as fundamental or base physical quantities and two as
(6) It should be universally acceptable. supplementary. These quantities are
Every measured quantity (its magnitude) comprises of a number
and a unit. Ex: In the measurement of time, say S.No Base physical quantity Fundamental unit Symbol
15 s 1 Mass kilogram kg
Number (n) Unit (u) 2 Length metre m
If Q is the magnitude of the quantity (which does not depend on 3 Time second s
the selection of unit) then
4 Temperature kelvin K
1
Q = n u = n1 u1 = n2 u2 Þ n µ 5 Electric current ampere A
u
6 Luminous intensity candela cd
Where u1 and u2 are the units and n1 and n2 are the numerical
values in two different system of units. 7 Amount of substance mole mol
, Units and Measurements 9
S.No Supplementary physical Supplementary unit Symbol Prefix Power of 10 Symbol
quantity exa 18 E
1 Plane angle radian rad
peta 15 P
tera 12 T
2 Solid angle steradian sr
giga 9 G
Merits of S.I. Units : mega 6 M
(1) SI is a coherent system of units: This means that all derived kilo 3 k
units are obtained by multiplication and division without hecto 2 h
introducing any numerical factor.
deca 1 da
(2) SI is a rational system of units: This is because it assigns
deci –1 d
only one unit to a particular physical quantity.
centi –2 c
(3) SI is an absolute system of units: There is no gravitational
unit in this system. milli –3 m
micro –6 m
(4) SI system is applicable to all branches of science.
nano –9 n
Conventions of writing of Units and their Symbols pico –12 p
· Unit is never written with capital initial letter.
femto –15 f
· For a unit named after scientist the symbol is a capital
letter otherwise not. atto –18 a
· The unit or symbol is never written in plural form. Some Important Practical Units :
· Punctuations marks are not written after the symbol. (1) For large distance (macro-cosm)
Definitions of Fundamental Units (a) Astronomical unit: It is the average distance of the
(i) Metre : One metre is equal to 1650763.73 wavelength in centre of the sun from the centre of the earth.
vacuum of the radiation corresponding to transition between 1 A.U. = 1.496 × 1011m
the levels 2p10 and 5d5 of the krypton – 86 atom (b) Light year: It is the distance travelled by the light in
Or vacuum in one year. 1 ly = 9.46 × 1015m
The distance travelled by light in vacuum in (c) Parsec: One parsec is the distance at which an arc
1A.U. long subtends an angle of one second.
1 1 parsec = 3.1 × 1016m
second is called 1 metre.
299,792, 458 (2) For small distance (micro-cosm)
(ii) Kilogram : The mass of cylinder (of height and diameter 1 micron = 10–6m 1nanometre = 10–9m
1angstorm = 10 m –10 1fermi = 10–15m
39 cm) made of Platinum-iridium alloy kept at International
Bureau of weights and measures in paris is defined as 1kg. (3) For small area 1 barn = 10–28m2
(iii) Second : It is the duration of 9,192,631,770 periods of (4) For heavy mass 1 ton = 1000kg
radiation corresponding to the transition between the two 1quintal = 100kg 1slug = 14.57kg
hyperfine levels of the ground state of Caesium (133) atom. 1 C.S.L (chandrasekhar limit) = 1.4 times the mass of the sun
(5) For small mass 1 amu = 1.67 x 10–27kg
(iv) Ampere : It is the current which when flows through two
1 pound = 453.6g = 0.4536 kg
infinitely long straight conductors of negligible cross-
(6) For small time 1 shake = 10–8s
section placed at a distance of one metre in air or vacuum
(7) For large time
produces a force of 2 × 10–7 N/m between them.
Lunar month: It is the time taken by the earth to complete
(v) Candela : It is the luminous intensity in a perpendicular one rotation about its axis with respect to sun.
direction, of a surface of 1/600,000 square metre of a black 1L.M. = 27.3 days.
body at the temperature of freezing platinum under a pressure Solar day: It is the time taken by the earth to complete one
of 1.013 × 105 N/m2. rotation about its axis with respect to sun.
(vi) Kelvin : It is the 1/273.16 part of thermodynamic temperature Sedrial day: It is the time taken by earth to complete one
of triple point of water. rotation on its axis with respect to distant star.
(vii) Mole : It is the amount of substance which contains as many (8) For measuring pressure
elementary entities as there are in 0.012 kg of Carbon-12. 1 bar = 1atm pressure = 105N/m2 = 760mmHg
S.I. Prefixes : 1torr = 1 mmHg
The magnitudes of physical quantities vary over a wide range. 1 poiseuille = 10 Poise.
For example, the atomic radius, is equal to 10 –10m, radius of earth DIMENSIONS
is 6.4×106 m and the mass of electron is 9.1×10–31 kg. The The powers to which the fundamental units of mass, length and
internationally recommended standard prefixes for certain powers time must be raised to represent the physical quantity are called
of 10 are given in the table: the dimensions of that physical quantity.
, EB
10 PHYSICS
For example : Force = mass × acceleration called dimensional formula. It shows how and which of the
fundamental quantities represent the dimensions.
v–u [LT -1]
= mass × = [M] T–2]
= [MLT For example, the dimensional formula of work is [ML2T–2]
t [T]
Hence the dimensions of force are 1 in mass 1 in length and (– 2) Dimensional Equation :
in time. When we equate the dimensional formula with the physical
Dimensional Formula : quantity, we get the dimensional equation.
Unit of a physical quantity expressed in terms of M, L and T is For example Work = [ML2T–2]
Classification of Physical Quantities (On the basis of dimensions) :
Dimensional Dimensional For e.g. c (velocity of light in vaccum)
physical quantity constant R(universal gas constant),
s(stefan's constant), h (Planck's constant),
k (Boltzmann constant), G (universal gravitational constant) etc.
Physical Dimensional For e.g. distance, displacement, force, mass, time etc.
Quantity variable
Dimensionless Dimensionless For e.g. 0, 1, 2, ....., e, p , sin q , cos q , tan q , etc.
physical quantity constant
Dimensionless For e.g. plane angle, solid angle, strain,
variable refractive index, dielectric constant, relative density,
specific gravity, poisson's ratio etc.
Dimensional Formula of Some Important Physical Quantities :
S.No. Physical quantity Relation with other quantities Dimensional formula
Length
1. Velocity (v) [M0LT–1]
Time
Velocity
2. Acceleration (a) [M0LT–2]
Time
3. Momentum (p) Mass × velocity [MLT–1]
4. Force (F) Mass × acceleration [MLT–2]
5. Work Force × displacement [ML2T–2]
6. Power (P) Work [ML2T–3]
Time
Fr 2
7. Universal gravitational constant G= [M–1L3T–2 ]
m1m 2
8. Torque t = r ´F [ML2T–2]
F
9. Surface tension S= [MT–2]
l
W
10. Gravitational potential VG = [M0L2T–2]
m
F
11. Coefficient of viscosity h= [ML–1T–1]
dv
A
dx
12. Impulse Force×time(F×t) [MLT–1]
