The Great India Rope Trick, Is this possible physically? I think it is impossible, but why can a magician be done.
Magic tricks are primarily about deception and misdirection. What you think is happening may not necessarily be happening. One explanation in the comments goes as follows:
The assistant fixing the basket (while audience are focused on the main actor) removed a cover from the ground then carefully fixed where a pipe clad with rope will comes out.
To actually answer your question, a simplified analogy to the supposed "rope" can be an inverted pendulum, where the end is above the fulcrum. Unless you orient it so that the pendulum is pointing exactly straight up with zero error, it will tip to one side, however slowly. As it tips to one side, its acceleration will increase. The rope can be thought of as many of these inverted pendulums stacked on top of each other. It's effectively impossible to keep a rope like this from falling down.