Physics behind Water drops during falling from a tap what is physics behind Water drops during falling from a tap.
water drop animation
A drop or droplet is a small column of liquid, bounded completely or almost completely by free surfaces.


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*Why Water drops falling into spheres (during falling from a tap in vacuum )?


please note that a drop of water made of $H_2O$ atoms.
Drop of water
 A: To mention it in a line, the shape of the liquid drop is spherical in vacuum due to Surface tension (Wikipedia link is better for an Intro)...
As Wikipedia says, the Cohesive forces of attraction between the liquid molecules (Weak hydrogen bonding is also possible) is the cause for Surface tension. Each molecule is pulled by the neighboring molecules resulting the net force to be zero. But, the molecules on the surface have no forces acting on them (Hence, no pulling). This causes the surface molecules to contract to a little extent.
But, the liquid drop's shape varies in presence of air or under free-fall due to gravity in air. See the possible Shapes of liquid drop. Probably, it has a shape of a semi-sphere with a flat or curved surface at the bottom which is due to the air-flow. This also explains the difference that smaller rain drops have more surface tension and mostly they have a perfect spherical shape, whereas comparatively larger drops have those flat or curved bottoms due to lower surface tension (since they have a larger area on the surface). Also, a raindrop has a critical limit. As it gets larger by combining with other drops, it has more possibilities for breaking..! For this reason, larger raindrops are often volatile (I mean "Temporary")
A: Surface tension and gravity are at work here. The surface tension minimizes potential energy when water forms a sphere and gravity acting on each and every molecule of water makes it fall. 
List of surface tension values for water in air.
