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A liquid drop placed on a horizontal plane has a near spherical shape (slightly flattened due to gravity). Let $\mathrm{R}$ be the radius of its largest horizontal section. A small disturbance causes the drop to vibrate with frequency $\mathrm{v}$ about its equilibrium shape. By dimensional analysis the ratio $\frac{\mathrm{v}}{\sqrt{\sigma / \rho \mathrm{R}^{3}}}$ can be (Here $\sigma$ is surface tension, $\rho$ is density, $\mathrm{g}$ is acceleration due to gravity, and $\mathrm{k}$ is arbitrary dimensionless constant)-
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$\mathrm{k} \rho \mathrm{gR}^{2} / \sigma$
$\frac{\mathrm{v}}{\sqrt{\sigma / \rho \mathrm{R}^{3}}}$ is dimensionless $\mathrm{k} \rho \mathrm{gR}^{2} / \sigma$ is also dimensionless
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