UNITS AND DIMENSIONS
The quantities by means of which we describe
the laws of physics are called physical quantities.
There are two type of physical quantities.
1 Fundamental quantities
the laws of physics are called physical quantities.
There are two type of physical quantities.
1 Fundamental quantities
2 Derived quantities
- 1 Fundamental quantities:
Physical quantities which are independent of each
other and cannot be further resolved into any
other physical quantity are known as fundamental
quantities. There are seven fundamental
quantities.
Fundamental Units Symbol
quantity(a) Length Metre m
(b) Mass Kilogram kg
(c) Time Second s
(d) Electric current Ampere A
(e) Thermodynamic Kelvin K
temperature
(f) Luminous Candela Cd
intensity
(g) Amount of Mole Mol.
substance
other and cannot be further resolved into any
other physical quantity are known as fundamental
quantities. There are seven fundamental
quantities.
Fundamental Units Symbol
quantity(a) Length Metre m
(b) Mass Kilogram kg
(c) Time Second s
(d) Electric current Ampere A
(e) Thermodynamic Kelvin K
temperature
(f) Luminous Candela Cd
intensity
(g) Amount of Mole Mol.
substance
- 2 Derived Quantities :
Physical quantities which depend upon
fundamental quantities or which can be derived
from fundamental quantities are known as derived
quantities.
fundamental quantities or which can be derived
from fundamental quantities are known as derived
quantities.
- UNITS
Definition : Things in which quantity is measured
are known as units.
Measurement of physical quantity
= (Magnitude) × (Unit)
Ex.1 A physical quantity is measured and the result
is expressed as nu where u is the unit used
and n is the numerical value. If the result is
expressed in various units then :(A) n ∝ size of u (B) n ∝ u2
(C) n ∝ u (D) n ∝ u
1
Answer : (D)There are three types of units
are known as units.
Measurement of physical quantity
= (Magnitude) × (Unit)
Ex.1 A physical quantity is measured and the result
is expressed as nu where u is the unit used
and n is the numerical value. If the result is
expressed in various units then :(A) n ∝ size of u (B) n ∝ u2
(C) n ∝ u (D) n ∝ u
1
Answer : (D)There are three types of units
Fundamental or base units
Derived units
Supplementary units
- Fundamental or base units:
Units of fundamental quantities are called
fundamental units.
fundamental units.
Characteristics of fundamental units:(i) they are well defined and are of a suitable size
(ii) they are easily reproducible at all places
(iii) they do not vary with temperature, time
pressure etc. i.e. invariable.
(iv) there are seven fundamental units.
(ii) they are easily reproducible at all places
(iii) they do not vary with temperature, time
pressure etc. i.e. invariable.
(iv) there are seven fundamental units.
Definitions of fundamental units:
Metre :The distance travelled by light in Vacuum in
1/299 ,792 ,458 seconds is called 1m.
1/299 ,792 ,458 seconds is called 1m.
Kilogram :The mass of a cylinder made of platinum iridium
alloy kept at international bureau of weights and
measures is defined as 1kg.
alloy kept at international bureau of weights and
measures is defined as 1kg.
Second :Cesium -133 atom emits electromagnetic radiation
of several wavelengths. A particular radiation is
selected which corresponds to the transistion
between the two hyperfine levels of the ground
state of Cs - 133. Each radiation has a time
period of repetition of certain characteristics. The
time duration in 9, 192, 631, 770 time periods of
the selected transistion is defined as 1s.
of several wavelengths. A particular radiation is
selected which corresponds to the transistion
between the two hyperfine levels of the ground
state of Cs - 133. Each radiation has a time
period of repetition of certain characteristics. The
time duration in 9, 192, 631, 770 time periods of
the selected transistion is defined as 1s.
Ampere :Suppose two long straight wires with negligible
cross-section are placed parallel to each other in
vacuum at a seperation of 1m and electric
currents are established in the two in same
direction. The wires attract each other. If equal
currents are maintained in the two wires so that
the force between them is 2 × 10–7 newton per
meter of the wire, then the current in any of the
wires is called 1A. Here, newton is the SI unit of
force.
cross-section are placed parallel to each other in
vacuum at a seperation of 1m and electric
currents are established in the two in same
direction. The wires attract each other. If equal
currents are maintained in the two wires so that
the force between them is 2 × 10–7 newton per
meter of the wire, then the current in any of the
wires is called 1A. Here, newton is the SI unit of
force.
Kelvin :The fraction
of 1/273.16
of the thermodynamic
temperature of triple point of water is called 1K.
of 1/273.16
of the thermodynamic
temperature of triple point of water is called 1K.
Mole :
The amount of a substance that contains as many
elementary entities (Molecules or atoms if the
substance is monoatomic) as there are number
of atoms in .012 kg of carbon - 12 is called a
mole. This number (number of atoms in 0.012 kg
of carbon-12) is called Avogadro constant and its
best value available is 6.022045 x 1023 .
The amount of a substance that contains as many
elementary entities (Molecules or atoms if the
substance is monoatomic) as there are number
of atoms in .012 kg of carbon - 12 is called a
mole. This number (number of atoms in 0.012 kg
of carbon-12) is called Avogadro constant and its
best value available is 6.022045 x 1023 .
Candela:
The S.I. unit of luminous intensity is 1cd which
is the luminous intensity of a blackbody of
surface area
1/600,000 m2
placed at the
temperature of freezing platinum and at a pressure
of 101,325 N/m2, in the direction perpendicular to
its surface.
The S.I. unit of luminous intensity is 1cd which
is the luminous intensity of a blackbody of
surface area
1/600,000 m2
placed at the
temperature of freezing platinum and at a pressure
of 101,325 N/m2, in the direction perpendicular to
its surface.
- Derived units :
Units of derived quantities are called derived units.
Physical quantity units
Physical quantity units
for example:Volume = (length)3 m3
Speed = length/time m/s
Speed = length/time m/s
Supplementary units :
The units defined for the supplementary quantities
namely plane angle and solid angle are called
the supplementary units. The unit for plane angle
is rad and the unit for the solid angle is steradian.
The units defined for the supplementary quantities
namely plane angle and solid angle are called
the supplementary units. The unit for plane angle
is rad and the unit for the solid angle is steradian.
- PRINCIPAL SYSTEM OF UNITS
2. F.P.S system [foot ; pound ; second]
3. M.K.S. system [meter ; kilogram ; second]
4. S.I. (system of international)
In 1971 the international Bureau of weight and
measures held its meeting and decided a system
of units. Which is known as the international
system of units.
In 1971 the international Bureau of weight and
measures held its meeting and decided a system
of units. Which is known as the international
system of units.
- DIMENSIONS
Dimensions of a physical quantity are the powers
to which the fundamental quantities must be
raised to represent the given physical quantity.
to which the fundamental quantities must be
raised to represent the given physical quantity.
for example:Force (Quantity) = mass × acceleration
= mass × velocity/time
= mass × velocity/time
= mass × length/(time)–2
= mass × length × (time)–2
so dimension in force : 1 in mass, 1 in length, –2 in time
and Dimensional formula : [MLT–2]
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