## Fundamental and Derived Units

Fundamental and Derived Units – (i) Fundamental units are those which are independent of each other and cannot be further resolved into any other units. All other units can be expressed in terms of these fundamental units. The quantities mass, length and time are called fundamental quantities. For measuring these quantities, these are independent units such as kilogram, meter and second.

(ii) For measuring other physical quantities, if a separate unit is defined for each of them, then it will become quite difficult to remember all of them because their number will be quite high. It is found that units of other physical quantities can be expressed in therms of the fundamental units of mass, length and time. The units of all such physical quantities which can be expressed in therms of the fundamental units of mass, length and time are called derived units.

(iii) For example, the unit of area is derived unit.the unit of area is area of a square having its length and breadth each equal to the unit length. The unit of volume is the volume of a cube having its all the sides of unit length. Actually, the unit of any physical quantity can be obtained from its defining equation e.g. let us consider the defining equation of speed.

*Speed=Distance traveled/time taken*

∴ Unit of speed = Unit of distance i.e. length/Unit of time=meter/second=m/s

### What is fundamental units to measure physical quantities?

The SI units of measurement of seven physical quantities are called fundamental units. The are: meter (m) for length, kilogram (kg) for mass, second (s) for time, ampere (A) for electric current, kelvin (K) for temperature candela (cd) for luminous intensity and mole (mol) for amount of substance.

Two more quantities are called supplementary units they are: radian (rad) for plane angle and steradian (sr) for solid angle.

### Characteristic of a Standered Units

Any standered unit selected for measuring a physical quantity must have the following properties :

(a)The standered unit must be well defined.

(b)The standered unit must be invariable.For example, defining distance between the tip of the middle finger and the elbow as a unit of length(called CUBIT, used earlier) is not invariable.

(c)The standered unit should be neither too small nor too large in comparison to physical quantities to be measured.

(d)The standered unit should be imperishable.

(e)Standered unit should be easily reproducible.

(f)The standered must not change with time, pressure temperature etc.

(g)The standered unit should be easily available for comparing with other quantities.

According to above requirements of standered units, the fundamental units of mass, length and time namely kilogram, metre and second have been defined as discussed bellow:

**Meter(m):** 1 metre is defined as the distance counting 1,650,763.73 wavelengths of the orange light emitted by pure Krypton-86.

**Kilogram(Kg):** 1 Kilogram is defined as the mass of a platinum-iridium cylinder kept at International Bureau of Weights and Measures in Paris. In practice, the mass of one litre of water at 4°C is 1 Kilogram. On atomic scale, 1 Kilogram is equivalent to the mass of 5.0188 ×10 ^{15} atoms of _{6}C^{12}(an isotope of carbon).

**Second(s):** Cesium-133 atom emits electromagnetic radiations of several wavelengths. A particular radiation is selected which corresponds to the transition between the two hyper fine 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 transition is defined as 1 s .