1.
A liquid drop placed on a horizontal plane has a near spherical shape (slightly flattened due to gravity). Let RR be the radius of its largest horizontal section. A small disturbance causes the drop to vibrate with frequency ν\nu about its equilibrium shape. By dimensional analysis the ratio ν2\nu^2 can be (Here σ\sigma is surface tension, ρ\rho is density, gg is acceleration due to gravity, and kk is arbitrary dimensionless constant):