Question

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

Answer 1

Answer:

Explanation:

hope it helps u

Answer 2

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^ykm

x

v

y

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

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

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

2

T

−2

]

Substitute both values of kinetic energy equal then we get

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

x

v

y

=[M][L

2

T

−1

]=[M

1

][(LT

−1

)

2

]

Comparing both sides we get :

x=1 and y=2

So, the formula becomes :

E=kmv^2E=kmv

2

Let k = 1/2

So,

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

2

1

mv

2

Hence, this is the required solution.