(i) She moved to the sink and turned on the water.
(ii) I bet you could really sink your teeth into that pork roast.
(iii) He also had a sink of responsibility about it.
i- this is correct. here, ‘sink’ means ‘a bowl that is attached to the wall in a kitchen or bathroom in which you wash dishes or your hands, etc.’. ii- this is correct. here, ‘sink’ means ‘to (cause something or someone to) go down below the surface or to the bottom of a liquid or soft substance’. iii- this is incorrect.