Mercury Splash

A mercury droplet of radius \(R=1~\mbox{mm}\) is released from a height h above the floor. After hitting the floor, the mercury droplet breaks into \(n=900\) identical spherical droplets. Find the minimum height \(h_{\text{min}}\) in centimeters for which such a splash is possible. The surface tension of mercury is \(\sigma=0.5~\mbox{N}/\mbox{m}\) and its density is \(\rho=13.5~\mbox{g}/\mbox{cm}^{3}\). The surface tension \(\sigma\) is defined as the energy required to increase the surface area of a liquid by a unit of area. Assume that the process is isothermal.

Details and assumptions

\(g=9.8~\mbox{m}/\mbox{s}^{2}\)

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