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Assume it sinks. In this case it will displace a volume of liquid, which is the same as to say that it will switch places with a volume of liquid. Hence a heavier volume of liquid will go up, and lighter volume of solid will go down. Do you see the issue? The issue is that this configuration does not minimize the energy of the system. So it will not sink.

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Yes, it will float. Floating is based on buoyancy. Which is not related to surface properties like friction of either the object or the fluid. The pressure causing the force keeping the object to keep floating is the hydrostatic pressure, also unrelated to surface properties; So it's about the pressure gradient you mention in the question. Interestingly, ...

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Maybe it would be useful to clear up a little bit the all thing : First of all, Bose-Einstein Condensation does not necessarily implies superfluidity: Bose-Einstein condensation (BEC) is characterized by a macroscopic occupation of a many-particle state $\Phi$ which correspond to the product of individual particle groud-states with zero-momentum ...

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I will answer your second question because it's the one with which I'm more familiar. The question we're answering is: "Why does current in a superconductor move with no resistance?" To understand this we should first understand why normal metals have nonzero resistivity. Imagine an electron in the metal and suppose it is traveling in some direction. If ...

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