Question

I know the formula I just don't know how derive it using dimetional analysis.​

Answer 1

Let the formula be [ MᵃVᵇ ] since kinetic energy depends on mass and velocity.

Kinetic energy is a form of energy and it can be written as [ ML²T⁻²] which is the dimensions of energy.

So we can equate both :

[ MᵃVᵇ ] = [ ML²T⁻²]

= > [MᵃLᵇT⁻ᵇ] = [ML²T⁻²]

We get a = 1 , b = 2

Hence K∝ mv²

⇒ K = cmv² where c is a constant.

Experimentally c=1/2 and hence ,

⇒ K = 1/2 mv²

[Proved]

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