Solving Buoyancy & Upthrust: Understand C & D

In summary, the force exerted by a liquid on a completely immersed solid can change depending on its depth and orientation. Option C and D are correct, while option A is not necessarily true for all liquid-solid pairs. The compressibility factor of liquids is higher than that of solids, but this does not apply universally. An example is mercury and hard rubber, where the rubber would not necessarily float in mercury due to its lower density. The problem statement only considers net buoyancy forces and is not constrained by the densities of the liquid and solid involved.
  • #1
Suraj M
Gold Member
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39

Homework Statement


A solid is completely immersed in a liquid. The force exerted by the liquid on the solid will(more than one right)
(a)increase if it is pushed deeper inside the liquid.
(b)change if its orientation is changed
(c)decrease if it is taken partially out of the liquid
(d)be in the vertically upward direction

Homework Equations



U=Vdlg

The Attempt at a Solution


Option C and D are true i got that, and the answers also say that the answer is C and D.
But why is Option A not true, the upthrust does increase when the solid is pushed down, right??
I just want to be sure. Thank you in advance
 
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  • #2
Suraj M said:
But why is Option A not true, the upthrust does increase when the solid is pushed down, right??
How do you propose that the force should increase?
 
  • #3
With depth there would be increase in pressure, as liquids have a higher compressibility factor than solids. Hence the density of the liquid would increase at a higher rate as compared to the solid. So the upthrust should increase, right?
 
  • #4
Suraj M said:
liquids have a higher compressibility factor than solids
Is this statement true for all possible liquid-solid pairs?
 
  • #5
I'm not sure. By you're tone, i guess it isn't true for all.
Could you give an example of a pair where this wouldn't be true‽
 
  • #6
Mercury ( ~ 3 ppm/atm) and let's say hard rubber.
 
  • #7
wouldn't rubber float in mercury?
 
  • #8
Suraj M said:
A solid is completely immersed in a liquid.
You could be using rubber coated uranium bricks; you're not constrained by liquid and solid densities in any way in the problem statement, you're merely calculating net buoyancy forces.
 
  • #9
oh ok. thank you!
 
Last edited:

Related to Solving Buoyancy & Upthrust: Understand C & D

1. What is buoyancy and upthrust?

Buoyancy and upthrust are related concepts in fluid mechanics that refer to the upward force exerted by a fluid on an object immersed in it. Buoyancy is the overall upward force exerted by a fluid on an object, while upthrust specifically refers to the upward force on an object that is partially or fully submerged in a fluid.

2. How is buoyancy and upthrust calculated?

Buoyancy and upthrust are calculated using Archimedes' principle, which states that the buoyant force on an object is equal to the weight of the fluid displaced by the object. This means that the buoyant force can be calculated by multiplying the density of the fluid, the volume of the displaced fluid, and the acceleration due to gravity.

3. What is the relationship between buoyancy and an object's density?

The relationship between buoyancy and an object's density is inverse - the more dense an object is, the less buoyant force it will experience in a fluid. This is because a more dense object will displace a smaller volume of fluid, resulting in a smaller buoyant force. Conversely, a less dense object will displace a larger volume of fluid and experience a greater buoyant force.

4. How does the shape of an object affect buoyancy and upthrust?

The shape of an object does not have a direct effect on buoyancy and upthrust. However, the shape can affect the amount of fluid displaced by the object, which in turn affects the buoyant force. A more streamlined object will displace less fluid and experience less buoyant force, while a more bulky or irregularly shaped object will displace more fluid and experience a greater buoyant force.

5. How is buoyancy and upthrust used in real life?

Buoyancy and upthrust have many practical applications in our daily lives. Some examples include: allowing boats and ships to float on water, helping hot air balloons and helium balloons rise into the air, and aiding in the design of submarines and other underwater vessels. Additionally, understanding buoyancy and upthrust is important in fields such as naval architecture, marine engineering, and oceanography.

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