Question

If density D ,frequency F and fundamental quantities then the dimemsiinal formula for kinetic energy should be?

Answer 1

Dimension of density, D = [ML^-3]

Dimension of frequency, F = [T^-1]

Dimension of velocity, V = [LT^-1] 

Kinetic energy, K = \(\frac{1}{2} mv^2\) = [ML²T^-2]

Let [k] = D^aF^bv^c

Then, [ML²T^-2] = [M^aL^-3a][T^-b][L^cT^-c]

[ML²T^-2] =  [M^aL^-3acT^-b-c]

Comparing the powers,

So, dimensional formula for kinetic energy should be [D¹F^-3v⁵] in terms of density, frequency and velocity.