What energy is decreasing in order to hold conservation of energy in the below mentioned case? There is a ball and a beaker. The beaker is filled with a liquid which has higher density than that of the ball. By the help of some mechanical force the ball is inserted inside the liquid and is made to touch the bottom of the beaker. Then the mechanical force acting on the ball is removed. Since the density of liquid is greater the ball starts to move to the surface and hence gains potential energy.
(Like in case of the roller coaster when the coaster reaches to the point of the loop where the coaster will be upside down position the kinetic energy decrease and potential energy increases and hence conservation of energy is fulfilled)
But in this case the buoyancy of the water will never decrease so if the potential energy is increasing in the ball then which energy is decreasing in order to hold conservation of energy.
Please guide me.
 A: The potential energy of the ball + liquid system decreases as the ball rises to the top of the container. When the mechanical force pushed the ball to the bottom of the beaker at the start, it did work against the buoyant force of the liquid, thereby storing potential energy in the system: you can call it the 'buoyant potential energy' if you want. The point is, after the force is removed, the buoyant potential energy decreases as the ball rises to the top, and this is converted into gravitational potential energy of the ball and kinetic energy of its motion.
Some of the initial potential energy may be lost as heat to the liquid as the ball moves through it and experiences viscous resistance.
A: As the ball rises to the surface of the liquid, the volume of liquid that was displaced by the ball will fall by the same distance that the ball has risen. Because the liquid is more dense than the ball, the mass of the displaced liquid is greater than the mass of the ball. Therefore the potential energy gained by the ball as it rises is less than the potential energy lost by the displaced liquid as it falls. The difference in energy is energy that is lost due to friction, turbulence in the liquid etc.
Another way to look at this is to see that the joint centre of mass of the ball and liquid together is raised when the ball is pushed to the bottom of the liquid, and the joint centre of mass falls when the ball rises to the surface again.
A: You seem to have missed an important point that *conservation of energy holds for a system only when there is  no external work being done  on the system. *
There is external force on the ball (the force of buoyancy and gravity)having positive work .Thus the total mechanical energy of ball may increase (or decrease )without violating the law of conservation of energy.
Yes, the ball gains potential energy as it rises but there's no reason for it to lose any energy . The extra energy it gains comes from the surrounding liquid.
If you take ball+ liquid as your system (@ gandalf61's  ans explained this  very well). The total energy is conserved .
