Water in a bucket is whirled in a vertical circle with a string attached to it. The water does not fall down even when the bucket is inverted at the top of its path. We conclude that in this position.
mg is not greater than
At topmost point draw free body diagram of water in the bucket and see.
Since its going in a circle, so a centripetal acceleration on it.
mg + N = mv2R
mg = mv2R−N
Now N ≥ 0