Surface Tension

A big water drop is formed by the combination of ?n? small water drops of equal radii. The ratio of the surface energy of ?n' drops to the surface energy of big drop is

When water is filled carefully in a glass, one can fill it to a height above the rim of the glass due to the surface tension of water. To calculate just before water starts flowing, model the shape of the water above the rim as a disc of thickness having semicircular edges, as shown schematically in the figure. When the pressure of water at the bottom of this disc exceeds what can be withstood due to the surface tension the water surface breaks near the rim and water starts flowing from there. If the density of water its surface tension and the acceleration due to gravity are and , respective, the value of in is ________