Question

1. A coin sinks in water.
2. A coin sinks in the water.
3. A coin sinks in the water of the glass.
4. A coin sinks in the sea [water].
5. A coin sinks in the river [water].
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[What about my explanation about 'water' and 'the water'?]
In #1 'water' is a generic term. In any water, a coin sinks. In #2, 'the water is the specific water such as #3, #4, and #5. So if 'water is used as a generic term, we need to use 'water.' If not, we need to use 'the water.' I mean 'the specific water'.

Answer 1

1 is fine.
2 - You don't need "the."
3 - It'd be better to say "... in the glass of water."
4 and 5 will be fine without using the word "water."

Yes, using "the" indicates a specific glass or unit or body of water.