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An object when released in water surface, just floats after getting fully submerged. Now taken to a greater depth, it is released. Will the body: (a) rise, (b) remains stable, (c) sink ?

My key doubts in answering are:

  • Arguments for (c): Will the density at all change with depth? Pure water is taken incompressible. And the solid object whose average density = 1 g/cm^3, can it get compressed at high pressures? I want to support this statement: The object can be made of silver (H.D. and non reactive, which is ideal) and the content has a lot of air, making the average density equal to that of water. Then at high depth won't the object become more dense?

  • Arguments for (a): Can this happen: The object will rise because it experiences higher pressure deep down, whereas internal pressure remains low, pulling it up. Thus even if F_b is constant, could the high pressure deep down prevent the object from going deep beyond a fixed level?

  • Arguments for (b): I think this is stronger argument than others. F_b is constant (water incompressible near surface of earth), pressure does not change the state of motion of an object, hence the equilibrium is maintained at any level.

So what is right? For reference, you can directly use these vars: rho = density of fluid, sigma = average density of object, g, m = mass of object, v = volume of displaced fluid = volume of object immersed (submerged completely), X = point on top surface of obj, Y = point on bottom surface, P_x, P_y, F_x, F_y (upward), F_b, W = v.rho.g, object is cuboid.

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2 Answers 2

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Bullet point 2 makes no sense. That's not how pressure works.

Water is a little bit compressible (though that's not relevant for the following):

We don't know what the object is: if it's incompressible, then it will float.

It could be made of water too, which means it remains neutrally buoyant.

It could undergo a phase transition due to pressure, in which case it would sink, or as combination of dense metal and a compressible gas, as you point out.

So the correct answers are $a, b, c$. The incorrect answers are $(b, c), (a, c), (a, b)$.

tl;dr that is a terrible question if you expect an answer, though it provides food-for-thought.

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  • $\begingroup$ Do you mean that based on further information, any option could be correct? What conditions will give the answer— the degree to which the solid or the water becomes more denser? How should the answer change if i say it is a Homogenous Alloy of R.D. = 1? With phase transition overriden. $\endgroup$
    – damnOk
    Commented Oct 31 at 18:09
  • $\begingroup$ @Swls Yes. It can be whatever you want it to be. $\endgroup$
    – JEB
    Commented Nov 3 at 13:38
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For your consideration:

In order for the object to rise when released at the greater depth, the upward buoyant force at that greater depth must be greater than it was at the lesser depth where the object floated stably just under the surface.

Since the buoyant force equals the weight of the volume of water displaced, and the volume of the water displaced is the same as long as the volume of the object remains the same, in order for the weight of the displaced water to be greater the density of water must increase at the greater depth.

Finally, the density of water is relatively constant. For example, at a depth of 1 mile below the surface of the ocean, sea water compresses by less than one percent).

Hope this helps.

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