Buoyant Force Problem

[CynicalBiochemist]

Homework Statement

Balls A and B of equal mass are floating in a swimming pool, as shown below. Which will produce a greater buoyant force?

a. Ball A

b. Ball B

c. Force will be equal

d. Impossible to determine without knowing the volume of each ball

In the picture given, it is clear that ball A has a greater volume than B.

Homework Equations

Fbuoyant=ρwater(Vwater displaced)g=ρwater(Vball)g

The Attempt at a Solution

I attempted this problem in 2 ways and got 2 different answers (A and C)

How I got Answer A:

Ball A has larger volume so it is clear that the buoyant force is greater

How I got Answer C:

If the balls are floating, then

mg=Fbuoyant

Since both balls have the same mass, it follows that they must generate the same buoyant force since both are floating and have the same weight.

The correct answer is A.

Please help me out. I don't understand why my second approach is flawed. Thanks in advance

 

[haruspex]

Ball A has larger volume so it is clear that the buoyant force is greater

You do not show the picture, but I am guessing the ball is partly out of the water. The buoyant force depends on the submerged volume.

How I got Answer C:
If the balls are floating, then
mg=Fbuoyant

Yes.

 

[Chestermiller]

I agree with OP. It’s C. The weight of the displaced volume of water will have to be mg.

 

[Charles Link]

@CynicalBiochemist One thing the question doesn't seem to be completely clear on: Are they interested in the buoyant forces when both balls are submerged, or are they asking you to compare the buoyant forces when both are floating? $\\$ When they ask "Which one produces...?", they need to specify the circumstances they want you to consider, or the question is very ambiguous.

 

[rude man]

@CynicalBiochemist One thing the question doesn't seem to be completely clear on: Are they interested in the buoyant forces when both balls are submerged, or are they asking you to compare the buoyant forces when both are floating? $\\$ When they ask "Which one produces...?", they need to specify the circumstances they want you to consider, or the question is very ambiguous.

"Balls A and B of equal mass are floating in a swimming pool".

 

[rude man]

I agree with OP. It’s C. The weight of the displaced volume of water will have to be mg.

Me too. But all you need is buoyancy force = mg. Sure, that force is also equal to the weight of the water displaced (Archimedes).

 

[Charles Link]

"Balls A and B of equal mass are floating in a swimming pool".

But the question says, "Which will produce a greater buoyant force?", and not " Which is producing a greater buoyant force?". They really would do well to clarify what are they asking the respondent to answer.

 

[rude man]

But the question says, "Which will produce a greater buoyant force?", and not " Which is producing a greater buoyant force?". They really would do well to clarify what are they asking the respondent to answer.

Not sure I appreciate the difference but then I only got about 3 hrs sleep last night!

 

[haruspex]

Not sure I appreciate the difference but then I only got about 3 hrs sleep last night!

The use of "will" implies a future behaviour rather than the present one, so under some other condition that needs to be specified; e.g., when pushed below the surface.
If the question has been stated exactly, word for word, in post #1 (@CynicalBiochemist, please confirm) then the omission of such a condition suggests it intends the present. On the other hand, the official answer suggests a changed circumstance.

 

[Merlin3189]

I can't see how you can consider changed circumstances, when the changed circumstances are not stated.
Perhaps they will be taken out of the water altogether.

 

[Charles Link]

I can't see how you can consider changed circumstances, when the changed circumstances are not stated.
Perhaps they will be taken out of the water altogether.

We're trying to make sense out of what appears to be an incorrect answer that was supplied to the question. It appears they may have wanted the student to work a different problem than what they actually stated.