Question

Derive the formula for kinetic energy of a particle having mass(m) and velocity(v) using dimensional analysis​

Answer 1

To find,

We need to derive the formula for kinetic energy of a particle using dimensional analysis.

Solution :

Let m is the mass and v is the velocity of the object.

Let kinetic energy of the particle is  

The dimensional formula of mass, [m]=[M]

The dimensional formula of velocity, [v]=[LT⁻¹]

Dimension of kinetic energy =

Substitute both values of kinetic energy equal then we get

Comparing both sides we get :

x=1 and y=2

So, the formula becomes :

Let k = 1/2

So,

Kinetic energy,