Question

Derive the formula for kinetic energy of a particle having mass m and velocity v using dimensional analysis
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Answer 1

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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

Answer:

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,  

Hence, this is the required solution.

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