# What Balances upthrust?

When a body is placed in a container containing some liquid, the liquid exerts an upthrust equal to the weight of the fluid displaced by the body.

I want to know which force balances this upthrust provided by the liquid. Is it the weight of body, the reaction force by container on the ground, or something else which I did not notice?

It is the weight of the body that balances the upthrust. You can understand it easily by drawing a free body diagram.

• If so then could you explain why if we weigh this(your diagram) on a weighing machine it reads weight of both ball and container rather than only container since upthrust is balanced by weight? Apr 12, 2017 at 7:39
• Ummm.. could you tell me if you understand the concept of normal reaction in solids correctly? If not then I'll start from there. I'll write another answer because I'll need to use diagrams too Apr 12, 2017 at 7:56

It is the weight of the body that balances the upthrust. You can understand it easily by drawing a free body diagram. Use Newtons third law and think.

• "use newtons third law and think" i dont know why im so amused haha Apr 11, 2019 at 22:04

It all depends what you mean by the word balances.
Are you looking for the force which makes the net force on the body zero, then that force is the weight of the the body.

Or are you looking for the Newton third law pair of forces?

Use Newton's third law to help identify which forces are acting on the body and the liquid.

The body in a fluid has a weight which is the force on the body due to the gravitational attraction of the Earth and the Newton third law pair to that is the force of attraction on the Earth by the body - both are non contact forces.

The other force the body has on it is the force due to the liquid, the upthrust, which is a contact force.
The Newton third law pair is the force that the body exerts on the liquid which is also a contact force.

Now consider the certainer with the liquid inside it.

There is the weight of the container and liquid (force on container and liquid due to the gravitational attraction of the Earth) with the Newton third law pair being the gravitational attraction on the Earth due to the liquid and the container.

There is the normal reaction of the scales on which the container is standing on the container and the liquid - this is equal to the reading on the scales.
That normal reaction force is equal in magnitude and opposite in direction (but not a Newton third law pair) to the force on the liquid due to the body (see above) plus the weight of the container and liquid because the net force on the container and water must be zero.

Consider the diagram above. For the body with mass M to be at rest the forces must be balanced. I've drawn a simple free body diagram and the forces acting on it are

1) Due to gravity in downward direction (Mg) 2) Due to the weight of the other object acting in the downward direction (mg) 3) Normal (reaction) force at the contact with scale in upward direction (N1)

To be at rest N1 must equal Mg + mg

what the weighing scale measures is the amount of force that it has to give to keep the body in contact with it in equilibrium in vertical direction. The weighing scale's plate must provide a force in the upward direction that will balance the downward force on M, hence keeping it in equilibrium. That force is provided by the normal reaction N1 acting on M.

The Normal force N2 is acting on m. It is trying to push m upwards. It is not pulling M upwards!

So if you replace N2 by the buoyant force and keep everything else same then you'll see that the buoyant force acts on the body, not on the water. Therefore, the weighing scale will measure the normal reaction N2 which is equal to Mg + mg.

I hope that clears your confusion.

In short, the buoyant force is not pulling the water upwards. It is pushing the body upwards.