# Buoyant Force Problem

• CynicalBiochemist
We're trying to make sense out of what appears to be an incorrect answer that was supplied to the question.

## 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)

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

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.

CynicalBiochemist said:
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.
CynicalBiochemist said:
If the balls are floating, then
mg=Fbuoyant
Yes.

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

@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.

@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".

Chestermiller said:
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).

rude man said:
"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.

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!

rude man said:
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.