Mercury Splash

A mercury droplet of radius R=1 mmR=1~\mbox{mm} is released from a height h above the floor. After hitting the floor, the mercury droplet breaks into n=900n=900 identical spherical droplets. Find the minimum height hminh_{\text{min}} in centimeters for which such a splash is possible. The surface tension of mercury is σ=0.5 N/m\sigma=0.5~\mbox{N}/\mbox{m} and its density is ρ=13.5 g/cm3\rho=13.5~\mbox{g}/\mbox{cm}^{3}. The surface tension σ\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 m/s2g=9.8~\mbox{m}/\mbox{s}^{2}

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