Bouyant Force Confusion

Question

I was asked to solve the question in the picture

I naturally thought the answer was (1) because bouyant force is caused by the pressure difference on the object's top and bottom surfaces.

Turns out that the answer is (3), can someone please explain me why is it (3), or is the book wrong in this case?

Please note that homework-like questions and check-my-work questions are generally considered off-topic here. We intend our questions to be potentially useful to a broader set of users than just the one asking, and prefer conceptual questions. Can you try making a question about some concepts that you'd need to solve this problem? — , Feb 16 '19 at 14:15
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While it would be possible to edit this question to make it on-topic, the on-topic version would certainly be a duplicate, e.g. of https://physics.stackexchange.com/q/62864/50583 — ACuriousMind, Feb 16 '19 at 14:44

score 5 · Answer 1 · answered Feb 16 '19 at 12:29

The water is producing an upward force on the ball (upthrust) equal to the weight of water displaced by the ball - Archimedes principle.

The ball must be exerting an equal in magnitude and opposite in direction force on the water - Newton’s third law.

The water is in static equilibrium and has two downward forces acting on it, its weight and the force due to the ball.
For the ball to static equilibrium it must have a net force of zero acting on it.
So there must be an upward force on the water due to the base of the beaker/balance equal in magnitude to the weight of the water and the downward force due to the ball.

Before the ball was added the beaker/balance exerted a force equal to the weight of the water.
With the ball immersed there is now an extra force exerted by the beaker/balance which is equal in magnitude to the weight of water displaced by the ball.

All I was confused about was ball exerting the downward force. Thanks for your clarification. — Kosh Rai, Feb 16 '19 at 12:40

Andrew Steane · Accepted Answer · 2019-02-16T12:53:35.780

(3) is right. The water partially supports the solid ball, exerting an upwards force equal to the weight of water displaced, which is 40 g if we take the density of water as 1 g per cm^3. So you can think of it as a case where the left side of the balance received this amount of extra weight.

It you want to think it through more fully, then, as you correctly say, this force on the ball is caused by the pressure difference on the upper and lower surfaces of the immersed ball. But notice that there is also this same amount of force acting downwards on the water! That might seem like an odd way of putting it, but it is what Newton's third law (action and reaction) says. Since the water is not accelerating, the beaker must be providing this amount of extra upwards force at the bottom surface of the water, in order to support the water. Hence the answer to the question.

Bouyant Force Confusion

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