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A foam is attatched to a concrete (both having different volume) by two inextensible wires. The entire system is submerged in water (in equilibrium), though not sunken, with the water just touching the surface of the foam and the wires stretched. Shouldn't the buoyant force acting on both be the same ? Considering that buoyant force arises from the 'push' of the displaced fluid, and that the fluid that is displaced by the bodies would not distinguish the bodies in applying the buoyant force, I think the buoyant force has got to be the same. [The displaced fluid wouldn't 'think' that the force needs to be dependent on the volume displaced by the body and so apply differently for bodies with different volumes]

But my Professor mentions that it isn't. It is equal to the weight of the fluid, occupying the 'volume of the respective bodies'.

Why is that ?

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  • $\begingroup$ „It is equal to the weight of the fluid, occupying the ‚volume of the respective bodies‘“ means it is the same, because the volume of the bodies are the same (this is what I read from your figure). So when your professor says „it isn’t“ than he/she contradicts him/herself in one sentence. I rather think, there is some misunderstanding. Maybe it is meant, that the net force, buoyancy plus gravity, is not equal because the buoyancy forces are equal but gravity isn‘t. $\endgroup$
    – Hartmut Braun
    Commented Sep 5, 2019 at 11:33
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    $\begingroup$ Suppose you cut the concrete block into two pieces, not necessarily both the same size, one hanging from each rope. Would you then claim the buoyant force on all three blocks should be equal, for the same reason? $\endgroup$
    – alephzero
    Commented Sep 5, 2019 at 11:33
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    $\begingroup$ @HartmutBraun the OP says "both having DIFFERENT volume". $\endgroup$
    – alephzero
    Commented Sep 5, 2019 at 11:34
  • $\begingroup$ Your professor is right. This is called the Archimedes' principle - see en.wikipedia.org/wiki/Archimedes%27_principle . $\endgroup$
    – Alex Trounev
    Commented Sep 5, 2019 at 11:37
  • $\begingroup$ @alephzero hmmmm, then it seems I misunderstood what OP meant. Now I’m confused: why does OP assume that „the fluid... does not distinguish...” if there is nothing that is the same for both bodies, neither height or volume or weight? $\endgroup$
    – Hartmut Braun
    Commented Sep 5, 2019 at 12:34

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When you say the water is "just touching the surface of the foam" I am going to assume you mean the top surface of the foam, so the foam is completely submerged.

If the foam and the concrete have different volumes then the buoyancy forces on them (when fully submerged) will also be different. The buoyancy force on each one is equal to the weight of the water that it displaces. The buoyancy forces are not changed by the wires joining the two objects. The wires will only change how much of the foam is submerged.

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