Force on the Bottom of the Vessel in Contact with the Cube

When a metal cube is placed in an empty vessel and water is filled in the vessel so that the cube is completely immersed, there will be a force exerted on the bottom of the vessel in contact with the cube. This force can be explained through the concept of buoyancy and the pressure exerted by the water.

Buoyancy
When an object is placed in a fluid, it experiences an upward force called buoyancy. This force is equal to the weight of the fluid displaced by the object. The metal cube, when immersed in water, displaces a certain volume of water equal to its own volume.

Pressure Exerted by the Water
The pressure of a fluid at a given depth is directly proportional to the height of the fluid column above that depth. This pressure is exerted in all directions, including upwards and downwards.

When the metal cube is immersed in water, the water exerts pressure on the cube from all sides. This pressure is highest at the bottom of the cube, as it is at the greatest depth within the water column. The pressure at the bottom of the cube is directly proportional to the height of the water column above it.

Force on the Bottom of the Vessel
The force on the bottom of the vessel in contact with the cube is a result of the pressure exerted by the water on the bottom surface of the cube. As the cube is completely immersed in water, the force on the bottom of the vessel is equal to the pressure exerted by the water on the bottom surface of the cube multiplied by the area of the bottom surface.

The force on the bottom of the vessel can be calculated using the following formula:
Force = Pressure × Area

The pressure can be determined by considering the height of the water column above the bottom surface of the cube, and the area is the same as the area of the bottom surface of the cube.

Therefore, when water is filled in the vessel so that the cube is completely immersed, the force on the bottom of the vessel in contact with the cube is determined by the pressure exerted by the water on the bottom surface of the cube.