A liquid drop placed on a horizontal plane has a near spherical shape (slightly flattened due to...

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A liquid drop placed on a horizontal plane has a near spherical shape (slightly flattened due to gravity). Let \( R \) be the radius of its largest horizontal section. \( A \) small disturbance causes the drop to vibrate with frequency \( v \) about its equilibrium shape. By dimensional analysis the ratio \( \frac{v}{\sqrt{\frac{\sigma}{\rho R^{3}}}} \) can be (Here \( \sigma \) is surface tension; \( \rho \) is density, \( g \) is acceleration due to gravity, and \( k \) is an arbitrary dimensionless constant)
[KVPY 2012]
(a) \( \frac{k \rho g R^{2}}{\sigma} \)
(b) \( \frac{k \rho R^{3}}{g \sigma} \)
(c) \( \frac{k \rho R^{2}}{g \sigma} \)
(d) \( \frac{k \rho}{g \sigma} \)
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