Answer:
v> √ gr
Step-by-step explanation:
Let's analyze this problem from Newton's second law
At the lowest point
N - W = m a
at the highest point
W = m a’
in both cases there is a net force towards the center of the circle that we can call the centripetal force, which is responsible for changing the direction and magnitude of the acceleration.
When the bucket is in the highest part, the centripetal force is equal to the weight of the water, but since it carries a horizontal speed, until it starts to fall, it is moving and therefore they follow the bottom of the tube. This implies that there is a minimum speed for this to occur
v> √ gr
This principle is applied in many things, for example the roller coaster, centrifuges, simulators of the effect of acceleration on people.