Question

A Bucket Containing Water Is Rotated In A Vertical Circle. Explain Why Water Does Not Fall ?

Answer 1

The centripetal force causes a body to follow a curved path. It always moves in the opposite direction of the body, towards the fixed point of the path's instantaneous centre of curvature. "A force by which things are pulled or pushed, or in any manner gravitate, towards a point as to a centre," wrote Isaac Newton. Gravity supplies the centripetal force that causes astronomical orbits in Newtonian mechanics.

Complete step by step solution:
When a bucket of water is just raised up and inverted, the water is strongly pulled by the force of gravity of the earth’s surface whereas there is no normal force below as there is no surface to limit fall of the water and therefore it falls
When someone rotates the bucket of water in the vertical circle, they are pushing the water away from their hand, towards the base of the bucket by a force which is directed away from their hand.
This force when balances gravity, the water would just be in the bucket. But when you spin the bucket this outward force named as Centrifugal force overcomes the gravity pull and pushes the water to the end of the bucket away from the opening of the bucket. So, it does not drop from the open end of the bucket.
Let v represent the bucket's velocity at the top of the circular route. A centripetal force ($\dfrac{{m{v^2}}}{R}$) is required to rotate the bucket of water in a vertical circle, where m is the mass of the water and R is the radius of the circular route. The centripetal force is provided by the weight of the water, therefore the water does not fall. In other words, the weight that prevents the water from falling is employed to provide the required centripetal force.

Note:
A centripetal force, as defined by Newton, corresponds to what is currently known as a central force. Gravity is regarded as a centripetal force when a satellite is in orbit around a planet, even if in eccentric orbits, the gravitational force is directed towards the focus rather than the immediate centre of curvature.