Cork in rotating water

The water is denser than the corks. As the turntable spins, the water will be pushed outwards with more force than the corks, thus displacing the corks towards the centre.

All the other solutions to this problem are pretty good, I just wanted to introduce the theory of negative mass ( relative), which behaves opposite to normal mass. As the corks act as negative mass in the denser water, the corks would move towards the centre, as opposed to normal mass which would turn away from the centre.

In order to counteract the force pushing them out, they will face inwards!

Consider the water-filled jar as the frame of reference. All the forces on the cork in the vertical direction are balanced due to the tension in the thread. When the turntable starts to rotate, for an observer inside the jar, there is an additional centrifugal acceleration acting on the jar system directed radially outward. This accelerated frame of reference is equivalent to a scenario as if gravity is acting in the horizontal direction. So, now we have a new pressure gradient created in the water along the horizontal axis. Since the cork is less dense than water, there will be a buoyant force acting on the cork directed radially inward towards the center of the turntable. Hence, the cork will tilt towards the center of the turntable. A similar experiment can be done by tying a helium balloon to the floor of a car with a thread. When the car accelerates from rest, the balloon deflects forward and not backwards, because the buoyant force of the surrounding fluid (air) dominates the effect of inertia of rest of the balloon.

Less dense objects move towards the direction of less pressure.since the table is rotating,pressure is high at the outer region than inner region. Hence the cork will move to less pressure region i.e towards the center.

In questions of this kind I often find it useful to add a horizontal outward force, equal in magnitude to the necessary inward centripetal force, so that we now have equilibrium. The effective gravitational force is the resultant of this imaginary force and the actual gravity, so its direction is downwards and outwards. Since the cork is lighter than the water the string will be in the opposite direction, i.e. upwards and inwards.

An alternative version of this question asked which direction the cork would move if the jars were only 1/3 full.

The suspended corks are buoyant in the water. This generates a force on the corks that is opposite in direction to the net force on the water.

At the beginning of the experiment (no rotation) the only force acting on the water is its weight, pointing downwards. The corks go up as far as they can.

When the table is rotating, centripetal force is acting on the water, pushing it outwards. The net force on the water changes direction to down- and outwards, the net force on the corks to up- and inwards.

Due to centrifugal force

It will move under inertia like this.

This is because when the table is rotating,the fluid inside the jar will be pushed outwards due to inertia.Since the cork is floating,the buoyant force acting on it must be greater than the weight of the cork.Imagine that the cork moves outwards with the fluid simultaneously,the fluid in it will be slightly compressed at the further side of the inner wall of the jar.As the fluid has been slightly compressed,the density of the fluid at the further side of the inner wall of the jar increases,hence the cork will only be required to displace a small amount of fluid in order to generate sufficient buoyant force to overcome the effect of inertia.Hence,the amount of fluid being displaced by the cork decreases and the cork seems to move inwards which I should towards the centre of the turntable