# 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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