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Can a hollow sphere float in a liquid?
Two spheres of the same mass and radius, but one hollow and other solid, float in a vessel containing a certain amount of liquid as shown in the diagram below. Would the height of liquid be the same in the two occasions?
How are hollow spheres and solid spheres the same?
The hollow sphere has a thick heavy rim that compensates for the air inside it – both spheres have the same mass and radius . Since the bodies have the same mass , the mass of liquid displaced is the same : . Hence the volume of liquid displaced is the same : . Hence the heights of liquid displaced are the same : .
Can a floating object sink to the same depth?
What you did is correct, two floating objects of identical mass will displace the same volume of water. If the surfaces of those objects have the same shape, then they will sink to the same depth.
How is the height of a liquid displaced?
(1) The mass of liquid displaced , so the height of liquid displaced (or height of solid under liquid) , where A is the area of cross section of the body and is the density of the liquid. Since all the three values remain the same on both occasions, the height of liquid displaced is the same : . (2) The average density of the solid object .
The key thing to notice is that Archimedes’ principle derives from the fact that the buoyant force acting on a body, which arises due to pressure forces of the liquid on the body that scale linearly with depth, is just proportional to volume submerged below the water level (with proportionality constant ).
Why does a block of wood float in water?
By Newton’s 3rd law, this bouyant force is also the force the body exerts on the liquid. Hence if the block of wood weighs more, it would also “push” down on the water and the vessel more, increasing the reading on its side of the weighing scale.