question_answer

A bucket of water is rotated in a vertical circle so that the surface of water is at a distance r from the axis of rotation. What is the minimum angular velocity so that the water does not spill out?

Answer:

                For water not to spill, weight of water must be balanced by centrifugal force\[\left( m\,r\,{{\omega }^{2}} \right)\]. i.e. \[\text{m r}\omega =\text{ mg}\],   \[\omega =\sqrt{g/r}\].