The number of physical quantities is quite large, but we need a limited number of units only for expressing all the physical quantities because they are interrelated with one another. Thus, we may define a set of fundamental (or base) quantities and all other quantities may be expressed in terms of these fundamental quantities. All other quantities are called derived quantities.
Units of fundamental and derived quantities are respectively, known as the fundamental units and derived units. A complete set of these units, both fundamental and derived units, is known as the system of units.
System of Units
The common system of units are
- FPS System The units of length, mass and time are respectively foot, pound and second.
- CGS System The units of length, mass and time are respectively centimetre, gram and second.
- MKS System The units of length, mass and time are respectively metre, kilogram and second.
SI System (International System of Units)
In 1971, CGPM held its meeting and decided a system of units which is known as the International System of Units. It is abbreviated as SI from the French name Le Systeme International d’ unites. This system is widely used through out the world.
The SI is based on the following seven fundamental units and two supplementary units.
| S. No | Quantity | Unit | Symbol |
|---|---|---|---|
| 1 | Mass | kilogram | kg |
| 2 | Length | metre | m |
| 3 | Time | second | s |
| 4 | Electric current | ampere | A |
| 5 | Temperature | kelvin | K |
| 6 | Amount of substance | mole | mol |
| 7 | Luminous intensity | candela | cd |
The two supplementary units in SI system are
- Radians for angle It is the angle subtended at the centre by an arc of a circle having a length equal to radius of the circle. Its symbol is rad.
- Steradians for solid angle It is the solid angle which has the vertex at the centre of the sphere, and cut-off an area of the surface of sphere equal to that of square with sides of length equal to radius of sphere.
Note
- Angle and solid angle are considered supplementary base units because although these have units but they are both dimensionless.
- 2 π radians = 360°
Metric Prefixes for Powers of 10
The physical quantities whose magnitude is either too large or too small can be expressed more compactly by the use of certain prefixes as given in the table.
| Power of 10 | Prefix | Symbol |
|---|---|---|
| 10-1 | deci | d |
| 10-2 | centi | c |
| 10-3 | milli | m |
| 10-6 | micro | µ |
| 10-9 | nano | n |
| 10-15 | femto | f |
| 10-18 | atto | a |
| 10-21 | zepto | z |
| 10-24 | yocto | y |
| 101 | deca | da |
| 102 | hecto | h |
| 103 | kilo | k |
| 106 | mega | m |
| 109 | giga | g |
| 1012 | tera | t |
| 1015 | peta | p |
| 1018 | exa | e |
| 1021 | zetta | z |
| 1024 | yotta | y |
Practical Units
A large number of units are used in general life for measurement of different quantities in comfortable manner. But they are neither fundamental units not derived units.
Some practical units are listed below
| S. No. | Practical Units of Length | Practical Units of Mass | Practical Units of Time |
|---|---|---|---|
| 1. | 1 light year = 9.46 x 1015 m | 1 quintal = 102 kg | 1 year = 365 1⁄4 solar days |
| 2. | 1 astronomical unit or 1 AU = 1.5 x 1011 m | 1 metric ton = 103 kg | 1 lunar month = 27.3 solar days |
| 3. | 1 parsec = 3.26 light year | 1 atomic mass unit (amu) = 1.66 x 10-27 kg | 1 solar day = 86400 s |
| 4. | 1 seamile = 6020 ft | 1 pound = 0.4537 kg | Tropical year it is that year in which solar eclipse occurs |
| 5. | 1 micron = 1 µm = 10-6 m | 1 chandrasekhar limit = 1.4 times the mass of sun = 2.8 x 1030 kg | Leap year it is that year in which the month of February has 29 days |
| 6. | 1 angstrom = 10-10 m | 1 slug = 14.59 kg | 1 shake – 10-8 s |
| 7. | 1 fermi = 10-15 m |
Sample Problem 1
What is the SI unit of surface tension ?
(a) Nm-1 (b) Nm-2 (c) Nm (d) N
Answer
(a) Surface tension = Force/Length = N/m = Nm-1
