IIT (NTSE/Olympiad)  

Unit, Dimension & Error


2.1 That fixed and definite quantity which we take as our standard of reference and by which we measure other quantities of same kind, is defined unit. There are of two types.
(a) Fundamental Units
(b) Derived Units
(a) Fundamental Units : The units which are independent and which are not be derived from other units, are defined as fundamental units. e.g. The unit of mass, length, and time.
There are seven fundamental units.
(i) Unit of mass
(ii) Unit of length
(iii) Unit of time
(iv) Unit of temperature
(v) Unit of electric current
(vi) Unit of luminous intensity
(vii)Unit of amount of substance
(b) Standard Units : The fixed and definite real value of any physical quantity is defined as standard unit.

2.2 Properties of Units :
The unit of a physical quantity is inversely proportional to its numerical value i.e., u ∝ 1/n where u and n are the units of physical quantity and its numerical value respectively. Relation between unit and its numerical value n1 u1 = n2 u2
2.3 Selection Criteria Of Units :
(i) Selected unit must be universal, of proper size and magnitude
(ii) Unit must be not affected by temperature, pressure and time.
(iii) Easily definable and reproducible.
2.4 System Of Units Used :
These are of Four types –
(i) C.G.S – (Centimeter – Gram – Second) system.
(ii) M.K.S. – (Metre – Kilogram – Second) system
(iii) F.P.S. – (Foot – Pound – Second) system
(iv) S.I. – (System – international) system
Following table will show the difference between all the systems.
Quantity C.G.S. M.K.S. F.P.S. S.I.(Symb.)
Mass gm kg pound kg
Length cm m foot metre
Time second sec sec second
Temperature kelvin kelvin kelvin (K)
Electric Current ampere ampere(A)
Luminous Intensity candela (cd)
Amount of substance mole(mol)

2.5 Supplementary Unit :
(a) Radian : → 1 radian is the angle subtended by arc of length equal to the radius, at the centre of the circle.
(b) Steradian : It is defined as the solid angle subtended at the centre of the sphere by an arc of its surface equal to the square of radius of the sphere.
Solid angle Ω = A/R2
when A = R2
Ω = 1 steradian

IIT (Class X)