Suppose i ask you "what is 5? what will be your answer? your answer would be " Are you kidding. Is not that obvious."
5 --- is a constant (or) number (or) numeric
10 , 15 20......???? all are numeric
The i add a post-fix to the constant like..
5 Kg .. what does it sense? It defines a mass or weight..
10 cm - Length
15 newton - force
20 hour / hr - time
PHYSICAL QUANTITY :
The quantities which can be measured are called Physical Quantity. Ex : Length , Mass , Time, Volume, Area , etc
UNIT :
The Standard of measurement of the physical quantity is called unit . Ex : meter, centi-meter, klio-meter are the unit of length.
SYSTEM :
A system of units defines a minimum number of physical quantities taken as fundamental to give a consistent and unambiguous description all physical quantity.
Is it requires for a common international forum of all scientist and engineers concern with measurement.
There are 4 system in use :-
1) C.G.S. system 2) F.P.S. system 3) M.K.S. system 4) S.I. system
1) F.P.S. System : The fundamental unit of length , mass, and time are respectively foot (ft), pound (p) and second (s).
2)M.K.S. System : The fundamental unit of length , mass, and time are respectively meter (m),kilo gram (kg) and second (s).
3)C.G.S. System : The fundamental unit of length , mass, and time are respectively centimeter (cm), gram (gm) and second (s).
4) S.I. System : ( International System of unit)
The S.I. units were approved by the C.G.P.M in 1960 and endorsed by both the ISO( International Organisational for Standardization ) and the IEC ( International Electrotechincal Comission ) in 1967.
The S.I unit consists of 7 base unit and 2 supplementary unit.
The S.I. unit are Coherent system of unit. i.e. all other physical quantity are derived from the S.I. units by simple multiplication and division without any numerical.
Base Unit (7)
1. Length - meter (m)
2. Mass - kilogram (kg)
3. Time - Second (s)
4. Temperature - kelvin (k)
5. Luminous Intensity - candela (cd)
6. Electric Current - ampere (A)
7. Amount of substance - mole (mol)
Supplementary Unit (2)
1. Plane angle - radian (rad)
2. Solid angle - steradian (sr)
Example : find the unit of velocity?
we know velocity = displacement / time
= m / s = ms-1
Some of the derived physical quantities are
DIMESIONS :
The dimension of a physical quantity are the powers to which fundamental unit must be raised to obtain the unit of that quantity.
DIMESIONAL FORMULA :
It is a formula which tells how and which of the fundamental units have been used for the measurement of that unit.
DIMESIONAL EQUATION :
An equation written in the following manner is called dimensional equation .
Example :
a) Area = length x breadth = [ L x L ] = [ L2] = [ M0L2T0 ]
1. Dimension of area is 0,2,0 of mass , length and time respectively
2. Dimensional Formula is [ M0L2T0 ]
3. Dimensional equation is Area = [ M0L2T0 ]
b) Acceleration = Velocity / Time = Displacement / time x (time) = Displacement / time 2
= L / T2 = [ M0L1T -2 ]
1. Dimension of area is 0,1,-2 of mass , length and time respectively
2. Dimensional Formula is [ M0L1T -2 ]
3. Dimensional equation is Velocity = [ M0L1T -2 ]
Steps for determination of dimension :
- Write the formula of the physical quantity of L.H.S. of the equation.
- Convert all the quantity of R.H.S. into the fundamental quantity Mass, Length and Time .
- Substitute M, L, and T for Mass, Length and Time respectively.
- Collect terms of M,L,T and find their resultant power which give the dimension of a quantity in Mass, Length and Time respectively.
Application of dimensional analysis :
- To check the correctness of a given relation .
- To convert the value of physical quantity from one system to another.
- To derive a relation between various physical quantity.
you can ask your queries by commenting below. I will try to solve your problem.
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