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 $km^xv^y$

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

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

Dimension of kinetic energy =$[M][L^2T^{-2}]$

Substitute both values of kinetic energy equal then we get

$km^xv^y=[M][L^2T^{-1}]=[M^1][(LT^{-1})^2]$

Comparing both sides we get :

x=1 and y=2

So, the formula becomes :

$E=kmv^2$

Let k = 1/2

So,

Kinetic energy, $E=\dfrac{1}{2}mv^2$

Hence, this is the required solution.

Answer 2

did you formula for kinetic energy of a particle having mass m and coelacity v using dimensional analysis answer is Up