Question

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

Answer 1

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We know, dimension of energy is, [E] = [M1L2T-2]

Dimension of mass is [m] = [M1L0T0]

Dimension of velocity is [v] = [M0L1T--1]

Suppose,

[E] = k [m]x [v]y

‘k’ is a proportionality constant which is a dimensionless quantity.

Therefore,

[M1L2T-2] = [M1L0T0]x [M0L1T--1]y

=> [M1L2T-2] = [MxLyT-y]

Thus, x = 1, y = 2

So, we have, E = k mv2

It is found that, k = ½

So, E = ½ mv2

It is found that, k = ½

So, E = ½ mv2

Derived....

Answer 2

Answer:

Energy is given in joules which is kg meter square per Second Square and since kinetic energy is also kind of energy it will have the same unit changing this unit in form of dimensions we get  

             

No the expression for kinetic energy is given as Changing this in form of dimensions  of M is mass, V is velocity is given by distance per unit time

          = = =

           From equation 1 and 2 we can say