My question is: when a cube is in perfect contact with the base of a beaker
containing fluid, and there is no fluid under the cube, will there be an upthrust on the cube?
If yes, then how do we derive out the upthrust expression?
If no, then wouldn't
Archimedes principle be violated as he mentioned that so long as there is fluid displaced,
there will be upthrust?
After a great deal of thought I
have the following comments.
(a) this is a theoretical question because no surface is
completely flat. Even on a polished metal cube there will be imperfections and bumps and
pits on the surface. This means that two surfaces are never in close contact over the whole
of their touching surfaces
(b) there will always be some water molecules that can "seep"
into the gaps between these bumps
However if we do assume that they can touch
over their whole surface then we have some interesting results.
It certainly does
appear that there will be no upthrust. If you draw a force diagram there will be no vertical
force due to liquid below the cube since there is no liquid below the cube. Think about a
situation where the cube is actually stuck to the base of the container. There is no upthrust in
this case.
An extension of this is to think of a hollow cube. If we follow the above
argument it mans that there is no upthrust on the hollow cube and therefore it would not float
up to the surface in spite of it having an average density less than that of
water.