UNITS AND MEASUREMENTS
The comparison of any physical quantity with its standard unit is called measurement.
Physical Quantities
All the quantities in terms of which laws of physics are described, and whose measurement is
necessary are called physical quantities.
Units
A definite amount of a physical quantity is taken as its standard unit.
The standard unit should be easily reproducible, internationally accepted.
Fundamental Units
Those physical quantities which are independent to each other are called fundamental
quantities and their units are called fundamental units.
S.No. Fundamental Quantities Fundamental Units Symbol
1. Length metre m
2. Mass kilogram kg
3. Time second S
4. Temperature kelvin kg
5 Electric current ampere A
6 Luminous intensity candela cd
7 Amount of substance mole mol
Supplementary Fundamental Units
Radian and steradian are two supplementary fundamental units. It measures plane angle and
solid angle respectively.
S.No. Supplementary Fundamental Quantities Supplementary Unit Symbol
1 Plane angle radian rad
2 Solid angle steradian Sr
Derived Units
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Those physical quantities which are derived from fundamental quantities are called derived
quantities and their units are called derived units.
e.g., velocity, acceleration, force, work etc.
Definitions of Fundamental Units
The seven fundamental units of SI have been defined as under.
1. 1 kilogram A cylindrical prototype mass made of platinum and iridium alloys of height
39 mm and diameter 39 mm. It is mass of 5.0188 x 1025 atoms of carbon-12.
2. 1 metre 1 metre is the distance that contains 1650763.73 wavelength of orange-red light
of Kr-86.
3. 1 second 1 second is the time in which cesium atom vibrates 9192631770 times in an
atomic clock.
4. 1 kelvin 1 kelvin is the (1/273.16) part of the thermodynamics temperature of the triple
point of water.
5. 1 candela 1 candela is (1/60) luminous intensity of an ideal source by an area of cm’
when source is at melting point of platinum (1760°C).
6. 1 ampere 1 ampere is the electric current which it maintained in two straight parallel
conductor of infinite length and of negligible cross-section area placed one metre apart
in vacuum will produce between them a force 2 x 10-7 N per metre length.
7. 1 mole 1 mole is the amount of substance of a system which contains a many elementary
entities (may be atoms, molecules, ions, electrons or group of particles, as this and atoms
in 0.012 kg of carbon isotope 6C12.
Systems of Units
A system of units is the complete set of units, both fundamental and derived, for all kinds of
physical quantities. The common system of units which is used in mechanics are given below:
1. CGS System In this system, the unit of length is centimetre, the unit of mass is gram
and the unit of time is second.
2. FPS System In this system, the unit of length is foot, the unit of mass is pound and the
unit of time is second.
3. MKS System In this system, the unit of length is metre, the unit of mass is kilogram and
the unit of time is second.
4. SI System This system contain seven fundamental units and two supplementary
fundamental units.
Relationship between Some Mechanical SI Unit and Commonly Used Units
S.No. Physical Quantity
Unit
1 Length
(a) 1 micrometre = 10-6 m
(b) 1 angstrom =10-10 m
2 Mass (a) 1 metric ton = 103 kg
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(b) 1 pound = 0.4537 kg
(c) 1 amu = 1.66 x10-23 kg
3 Volume
1 litre = 10-32 m3
4. Force
(a) 1 dyne = 10-5 N
(b) 1 kgf = 9.81 N
5. Pressure
(a) 1 kgfm2 = 9.81Nm-2
(b) 1 mm of Hg = 133 Nm-2
(c) 1 pascal = 1 Nm-2
(d) 1 atmosphere pressure = 76 cm of Hg = 1.01 x 105 pascal
6. Work and energy
(a) 1 erg =10-7 J
(b) 1 kgf-m = 9.81 J
(c) 1 kWh = 3.6 x 106 J
(d) 1 eV = 1.6 x 10-19 J
7. Power
(d) 1 kgf- ms-1 = 9.81W
1 horse power = 746 W
Some Practical Units
1. 1 fermi =10-15 m
2. 1 X-ray unit = 10-13 m
3. 1 astronomical unit = 1.49 x 1011 m (average distance between sun and earth)
4. 1 light year = 9.46 x 1015 m
5. 1 parsec = 3.08 x 1016 m = 3.26 light year
Some Approximate Masses
Object Kilogram
Our galaxy 2 x 1041
Sun 2 x 1030
Moon 7 x 1022
Asteroid Eros 5 x 1015
Dimensions
Dimensions of any physical quantity are those powers which are raised on fundamental units to
express its unit. The expression which shows how and which of the base quantities represent
the dimensions of a physical quantity, is called the dimensional formula.
Dimensional Formula of Some Physical Quantities
S.No.
Physical
Quantity
Dimensional
Formula
MKS
1 Area [L2] metre2
2 Volume [L3] metre3
3 Velocity [LT-1] ms-1
4 Acceleration [LT-2] ms-2
5 Force [MLT-2] newton (N)
6 Work or energy [ML2T-2] joule (J)
7 Power [ML2T-3] J s-1 or watt
8 Pressure or stress [ML-1T-2] Nm-2
9 Linear momentum or Impulse [MLT-1] kg ms-1
10 Density [ML-3] kg m-3
11 Strain Dimensionless Unitless
12 Modulus of elasticity [ML-1T-2] Nm-2
13 Surface tension [MT-2] Nm-1
14 Velocity gradient T-1 second-1
15 Coefficient of velocity [ML-1T-1] kg m-1s-1
16 Gravitational constant [M-1L3T-2] Nm2/kg2
17 Moment of inertia [ML2] kg m2
18 Angular velocity [T-1] rad/s
19 Angular acceleration [T-2] rad/S2
20 Angular momentum [ML2T-1] kg m2S-1
21 Specific heat L2T-2θ-1 kcal kg-1K-1
22 Latent heat [L2T-2] kcal/kg
23 Planck’s constant ML2T-1 J-s
24 Universal gas constant [ML2T-2θ-1] J/mol-K
Homogeneity Principle
If the dimensions of left hand side of an equation are equal to the dimensions of right hand side
of the equation, then the equation is dimensionally correct. This is known as homogeneity
principle.
Mathematically [LHS] = [RHS]
Applications of Dimensions
1. To check the accuracy of physical equations.
2. To change a physical quantity from one system of units to another system of units.
3. To obtain a relation between different physical quantities.
Significant Figures
In the measured value of a physical quantity, the number of digits about the correctness of
which we are sure plus the next doubtful digit, are called the significant figures.
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