Dimension Analysis

1.Dimension
When derived quantity is expressed in terms of fundamental quantity, it is written as a product of different power of the fundamental quantities.

The exponent of base quantity that enter into the expression of physical quantity is called dimensions.
For example :- dimension formula of force. 
 Method :-
                     Force = mass×acceleration
                               =(mass×velocity)÷time
                              =mass×length÷time^2
                             =mass×length×time^-2 
 Dimension formula of Force  =[MLT^-2]
 2. Application of dimensional analysis.
1). To find the unit of physical quantity or constant.
Example :-
            1.Work = force×displacement 
                    W = [M L T^-2]×[L]
                    [W ]= [M L^2 T^-2]
    S.I unit of work = kg m^2 s^-2.
                  
           2. Gravitational force(F) 
                                  = GmM/r^2
                    G = Fr^2/mM
                   [G]=[MLT^-2][L^2]/[M][M]
                   [G] = [M^-1 L^3 T^-2]
    S.I unit of G = kg^-1 m^3 s^-2
We can find unit of any quantity or constant by using dimensions.
M,L,T is mass,length,time respectively has fundamental unit.
2). To convert a physical quantity from one system to another system.

Example :-

3). To Check the dimension correctness of the physical relation. 
Also called principle of  homogeneity.
If the given equation is dimensionally correct then it is valid and vice versa.
Example :-

4). To establish the relation between different physical quantities. 
Example :-

3. Limitation of dimensional analysis
1). Numerical constant cannot have dimension such as π,2π and ect. 
    Example :- Area of circle = πr^2
    Dimension formula =[L^2]
 2). Trigonometric constant cannot have dimension such as cos(theta),sin(theta) and etc.
4.Some Important dimensions formulas

 You should learn dimension formula of force and velocity so, you can easily derived all other dimensions formula by just learning their formula.

Thankyou very much.
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In next session, we can do some questions which is commenly asked in IIT JEE and some concept building questions.