Buoyancy: Will the Object float or sink or remain at a depth?

[SpectraPhy09]

Homework Statement

A body is just floating on the surface of a liquid. The density of the body is same as that of the liquid. The body is slightly pushed down. What will happen to the body?
a) It will come back slowly to its earlier position
b) It will remain submerged where it is left
c) It will sink
d) It will come out violently

Relevant Equations

Buoyancy Force = ρgh
ρ = density of the liquid

My answer was coming b but it's given wrong in my textbook.
Because if a body is submerged completely in a liquid then
buoyancy Force = mg
So if the net force is Zero then shouldn't the body remain there?
Plz can someone tell where did i went wrong?
Also can a body float inside a liquid Because I never Saw such things before I think it will either sink on float on the surface

 

[BvU]

Hi,

If the book says abswer b) is wrong, what would you consider the best of the remaining answers ?

Also can a body float inside a liquid

Submarines and fish do it all the time !

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[jbriggs444]

Homework Statement:: A body is just floating on the surface of a liquid. The density of the body is same as that of the liquid. The body is slightly pushed down. What will happen to the body?
a) It will come back slowly to its earlier position
b) It will remain submerged where it is left
c) It will sink
d) It will come out violently
Relevant Equations:: Buoyancy Force = ρgh
ρ = density of the liquid

My answer was coming b but it's given wrong in my textbook.
Because if a body is submerged completely in a liquid then
buoyancy Force = mg
So if the net force is Zero then shouldn't the body remain there?
Plz can someone tell where did i went wrong?
Also can a body float inside a liquid Because I never Saw such things before I think it will either sink on float on the surface

At a guess, the book is asserting that answer c) is correct because the object will be compressed slightly as it sinks and, so, will have a tendency to become less buoyant and sink further. This argument is incorrect because we are not told whether the body is more compressible, less compressible or equally compressible than water.

A correct response will assume that the difference in compressibility is negligible. This makes your chosen answer, b), correct.

A body can float in a stable fashion inside a depth of water if the body is less compressible than water and has a density that matches that of water at some accessible depth.

[I feel free to hand out answers rather than asking leading questions because, in my opinion, you have already answered the problem correctly].

 

[haruspex]

Homework Statement:: A body is just floating on the surface of a liquid. The density of the body is same as that of the liquid. The body is slightly pushed down. What will happen to the body?
a) It will come back slowly to its earlier position
b) It will remain submerged where it is left
c) It will sink
d) It will come out violently
Relevant Equations:: Buoyancy Force = ρgh
ρ = density of the liquid

My answer was coming b but it's given wrong in my textbook.
Because if a body is submerged completely in a liquid then
buoyancy Force = mg
So if the net force is Zero then shouldn't the body remain there?
Plz can someone tell where did i went wrong?
Also can a body float inside a liquid Because I never Saw such things before I think it will either sink on float on the surface

I don't like this question, there are so many uncertainties.

"A body is just floating on the surface of a liquid". What does that mean? It clearly does not mean it is ON the surface. Maybe AT the surface, but water, e.g., has surface tension, so is the top of the object wet? It makes a difference.

"The density of the body is same as that of the liquid." In reality, it cannot be exactly the same, but leaving that aside, real liquids are not completely incompressible, so their density increases slightly with depth. If the body's density exactly matches that of the water at the surface it will always return to the surface.
On the other hand, the body will be compressible. If more compressible than the liquid it will continue to sink.

"The body is slightly pushed down." Is that as in "given a push", or as in moved down a little? In the former case it has momentum, so if exactly neutral buoyancy it will continue to drift down. In the latter case it will not.

The most reasonable set of assumptions and idealisations leads to b), so I would be interested to learn what answer the book gives and with what explanation.

Edit: I see @jbriggs444 beat me to it. Reassuring that we agree.

Submarines and fish do it all the time !

But only by a combination of active swimming and active buoyancy control.

 

[Orodruin]

A body can float in a stable fashion inside a depth of water if the body is less compressible than water and has a density that matches that of water at some accessible depth.

Reversely, if a body has higher compressibility, the equilibrium point exists but is unstable. This is particularly important in scuba diving where an inflatable jacket is used to regulate buoyancy. It is important to regulate your net buoyancy to be neutral when the jacket is empty (typically by adding weights to your weight belt) because air is highly copressible and will make your position very unstable. Rising or descending too fast when diving is generally a very bad idea.

 

[BvU]

Poor @SpectraPhy09 : a harmless looking exercise in an introductory chapter (correct me if I am wrong*) and then such an accumulation of complications.

(*) of course we know nothing about the context, so we create our own. In my case I suspected the exercise composer wanted answer c) : the pushing gives the block downward momentum which is conserved if it isn't dissipated by viscosity. Admittedly not very realistic.

But I think we can all agree it's a poor and incompletely formulated exercise

$\$

 

[SpectraPhy09]

would you consider the best of the remaining answers ?

I think that ans A might be correct because when the body is pushed some force must be applied so it would have a net upward acceleration and it will come back to its initial position. Plz correct me if I'm wrong.

At a guess, the book is asserting that answer c)

Yes given ans is C. Sorry but I didn't got your explanation about compressibility since I don't know much about it (Actually nothing)

The most reasonable set of assumptions and idealisations leads to b), so I would be interested to learn what answer the book gives and with what explanation.

Given ans is C. But I'm confuse about a & b. I'm not getting how it can be c .

If the body's density exactly matches that of the water at the surface it will always return to the surface.

Yes I also think the Same.

 

[SpectraPhy09]

a harmless looking exercise in an introductory chapter

Yes Correct.

 

[jbriggs444]

I think that ans A might be correct because when the body is pushed some force must be applied so it would have a net upward acceleration and it will come back to its initial position. Plz correct me if I'm wrong.

I do not understand your argument here. You apply a downward force and expect an upward acceleration?!

My understanding is that the object starts completely immersed except that the very top is even with the top of the water. You push it down. Why would you expect a rebound?

This may go over your head, but I will try...

In general, one expects a rebound if there is a stable equilibrium. Stable equilibria are common in day to day life. You push something and it springs back after you stop pushing. But not all equilibria are stable. If you have a ball sitting on the top of a hill and you push it, it will not spring back to the top of the hill when you stop pushing.

Yes given ans is C. Sorry but I didn't got your explanation about compressibility since I don't know much about it (Actually nothing)

Suppose that the object is pushed slightly underwater. The water pressure down there is greater than that at the surface, yes?

Even solid objects compress slightly when you squeeze them. So what happens to the volume of an object when it is subject to increased pressure?

 

[SpectraPhy09]

I do not understand your argument here. You apply a downward force and expect an upward acceleration?!

Yes I got your point here . So if it is pushed downward then it should have an downward acceleration so it will sink, right? This means option C should be correct.

The water pressure down there is greater than that at the surface, yes?

Yes, Pressure increases as depth increases . So if pressure increases then force due to the liquid acting on the object should also increase so this means that It should get compress. Is this what you mean?(please correct if I'm Wrong) .
So if the volume decreases then buoyancy force should also decrease right ? So this means the object will sink ? I.e option C.

 

[Orodruin]

Yes, Pressure increases as depth increases . So if pressure increases then force due to the liquid acting on the object should also increase so this means that It should get compress. Is this what you mean?(please correct if I'm Wrong) .
So if the volume decreases then buoyancy force should also decrease right ? So this means the object will sink ? I.e option C.

Depends on the object’s compressibility relative to that of water. If it is less compressible the water density will increase faster and buoyancy will increase.

 

[jbriggs444]

Yes I got your point here . So if it is pushed downward then it should have an downward acceleration so it will sink, right?

But when you remove the force, the acceleration ceases, right? So now we have an object with a downward velocity. What happens next?

This is the scenario suggested by @BvU in post #6 above: All other things being equal, the downward velocity will be damped by viscosity -- if we are supposed to consider viscosity.

The further difficulty is that we cannot be sure that all other things are equal. Hence our concerns about compressibility.