Question

If density D, frequency F and velocity V are taken as fundamental quantities then the dimensional formula for kinetic energy shoul be?

Answer 1

Answer:

1/2 × (mass)× (velosity)2 I hope this will help you

Answer 2

Dimension of frequency , F = [T⁻¹]

Dimension of velocity ,V = [LT⁻¹]

Dimension of density , D = [ML⁻³]

Dimension of momentum , P = [MLT⁻¹]

Let relation between P with F, V and D is given by

P = FᵃVᵇDˣ

[MLT⁻¹] = [T⁻¹]ᵃ[LT⁻¹]ᵇ[ML⁻³]ˣ

[MLT⁻¹] = [Mˣ][Lᵇ⁻³ˣ][T⁻ᵃ⁻ᵇ]

Compare both sides,

x = 1 , b - 3x = 1 and -a - b = -1

b = 3x + 1 = 4

a = 1 - b = -3

Hence, P = F⁻³V⁴D¹