The frequency (ν) of an oscillating liquid drop may depend upon radius (r) of the drop, density (ρ) of liquid and the surface tension (s) of the liquid as : ν = rᵃρᵇsᶜ. The values of a, b and c respectively are
Options

Question

The frequency (ν) of an oscillating liquid drop may depend upon radius (r) of the drop, density (ρ) of liquid and the surface tension (s) of the liquid as : ν = rᵃρᵇsᶜ. The values of a, b and c respectively are

Options

G1 Physics · Accepted Answer

Dimensions are [ν] = T⁻¹, [r] = L, [ρ] = ML⁻³ and [s] = MT⁻². Thus T⁻¹ = Lᵃ(ML⁻³)ᵇ(MT⁻²)ᶜ. Comparing powers gives b + c = 0, -2c = -1 and a - 3b = 0. Hence c = 1/2, b = -1/2 and a = -3/2.