Question

Give relation for kinetic energy of vody of mass m and moving with velocity using dimensional analysis

Answer 1

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

Derived.