# Units and Dimensions

Every measurement has two parts. The first is a number (n) and the next is a unit (u). Q = nu. For example, Length of an object = 35 cm. The number expressing the magnitude of a physical quantity is inversely proportional to the unit selected.

If n1 and n2 are the numerical values of a physical quantity corresponding to the units u1 and u2, then n1u1 = n2u2. For example, 2.8 m = 280 cm; 6.2 kg = 6200 g

The quantities that are independent of other quantities are called fundamental quantities. The units that are used to measure these fundamental quantities are called fundamental units.

There are four systems of units:

1. C.G.S - Centimetre, Gram, Second
2. M.K.S - Metre, Kilogram, Second
3. F.P.S - Foot, Pound, Second
4. SI

The quantities that are derived using the fundamental quantities are called derived quantities. The units that are used to measure these derived quantities are called derived units.

Fundamental Physical Quantities in SI System

 Physical Quantity Unit Symbol Length metre m Mass kilogram kg Time second s Electric current ampere A Thermodynamic temperature kelvin K Intensity of light candela cd Quantity of substance mole mol

Supplementary Quantities in SI System

Metre: A metre is equal to 1650763.73 times the wavelength of the light emitted in vacuum due to electronic transition from 2p10 state to 5d5 state in Krypton-86. But in 1983, 17th General Assembly of weights and measures, adopted a new definition for the metre in terms of velocity of light. According to this definition, metre is defined as the distance travelled by light in vacuum during a time interval of 1/299, 792, 458 of a second.

Kilogram: The mass of a cylinder of platinum-iridium alloy kept in the International Bureau of weights and measures preserved at Serves near Paris is called one kilogram.

Second: The duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of caesium-133 atom is called one second.

Ampere: The current which when flowing in each of two parallel conductors of infinite length and negligible cross-section and placed one metre apart in vacuum, causes each conductor to experience a force of 2x10-7 newton per metre of length is known as one ampere.

Kelvin: The fraction of 1/273.16 of the thermodynamic temperature of the triple point of water is called kelvin.

Candela: The luminous intensity in the perpendicular direction of a surface of a black body of area 1/600000 m2 at the temperature of solidifying platinum under a pressure of 101325 Nm-2 is known as one candela.

Mole: The amount of a substance of a system which contains as many elementary entities as there are atoms in 12x103 kg of carbon-12 is known as one mole.