I expect that if you actually ran this experiment, the answer would be a point because the ice cube would stop swinging before all that much melting had occurred. Additionally, even in situations where the ice cube swings indefinitely along an unchanging trajectory, warm sand evaporates drops of water quite quickly, so a trajectory that isn’t a line would probably end up a fairly odd shape.
This is all because ice melting is by far the slowest of the things that are relevant for the problem.
I expect that if you actually ran this experiment, the answer would be a point because the ice cube would stop swinging before all that much melting had occurred. Additionally, even in situations where the ice cube swings indefinitely along an unchanging trajectory, warm sand evaporates drops of water quite quickly, so a trajectory that isn’t a line would probably end up a fairly odd shape.
This is all because ice melting is by far the slowest of the things that are relevant for the problem.