# 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)

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.

Homework Helper
Gold Member
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.
If the balls are floating, then
mg=Fbuoyant
Yes.

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

• Homework Helper
Gold Member
@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.

Homework Helper
Gold Member
@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".

Homework Helper
Gold Member
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).

Homework Helper
Gold Member
"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.

Homework Helper
Gold Member
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! • Homework Helper
Gold Member
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.

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