Question

How to find dimension of any thing like of kinetic energy and potential energy
Please explain it

Answer 1

Equate 1/2 mv^2 with energy
1/2 mv^2= E
Write dimensions on both sides,
ML^2T^-2= ML^2T^-2
Hence proved!

Answer 2

first you have to know about the fundamental unities . 
Mass = kilogram which is kg 
Length = Length  which is in m 
Time = Time  which in sec 
Temperature = K which in kelvin 
Electric current  =  A which in ampere 
Luminous intensity = cd which is  candela 
Quantity of matter = mole is mol 

now energy 

k.e = 1/2 mv² 

here we know that 

1/2 is a constant 

m =mass = M 

and v = velocity = displacement/ time = length / time = L T⁻¹

now K.e = M ( LT⁻¹ ) ²
             =  M L² T⁻²

NOW IN THE CASE OF THE POTENTIAL ENERGY 

energy (P ) = mgh 

here m = mass = M 
g = acceleration due to gravity  = L T⁻²
h = HEIGHT = length = L 
now 
energy (P ) = M ( LT⁻² ) L
                  = M L² T⁻²
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