Question

how to find dimentional formula of kinetics energy ?

Answer 1

si unit of kinectic energy's is joule . in fundamental units joule is kgm²s^-2. there a there is power 1 on mass unit, power 2 on lenght unit,power -2 on time unit. hence dimensional formula is [M^1L^2T^-2].
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Answer 2

Hey there !!!!!

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Any physical quantity like energy,force,power can be written in the form of dimensions in terms of Mass(M), Length(L), Time(T) 

Kinetic Energy = (Mass)(Velocity)²/ 2

                       = (Mass)(Distance/time)²/2

Dimensional formula of mass= M , distance=L , time = T

When we write a dimensional formula of a quantity we neglect the constants i.e, in this case "2"

So dimensional formula of Kinetic energy : 

           Kinetic Energy = (Mass)(Velocity)²/ 2

                                  = (Mass)(Distance/time)²/2
                          
                                  =(M)(L/T)²=[ML²T⁻²]

So dimensional formula of kinetic energy = [ML²T⁻²]

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Hope this helped you.....................