a drop of ink is placed gently at the base of beaker containing water by means of a dropper . What will happen

Ink will mix with water solution. After sometime you cannot distinguish ink and water.
These observation indicates that there are intermolecular spaces in between the water molecules to accommodate ink molecules.
Particles of matter are always in motion, this helps to spread ink molecule through the water solution.
 

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the ink diffuses into the entire liquidEven though ink is more dense than water, it is still partially miscible ( mixes well ) in water.

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