A vessel filled with two liquid how to determine boant force?

[vkash]

A vessel filled with two liquid how to determine boyant force?

A vessel contains oil of density(800kgm^-3) over mercury (density 13600kgm^-3) A homogeneous Sphere is floats with half of its volume immersed in mercury and other half in oil. What is density of the material of the sphere?

How to apply Archimedes principle of floating? can you please help.

 

[ehild]

What does Archimedes' Principle say? ehild

 

[vkash]

What does Archimedes' Principle say?


ehild

It says that buoyant force is equal to weight of liquid displaced.

 

[ehild]

There are two kinds of liquid displaced. What is the volume and the weight of each when the volume of the sphere is V?

ehild

 

[vkash]

There are two kinds of liquid displaced. What is the volume and the weight of each when the volume of the sphere is V?

ehild

But lighter liquid seems to push the sphere downward rather than pushing it upward. and lower liquid seems to push with greater power.
even after this. can i apply that principle?

 

[ehild]

You get upward force at the bottom of the immersed volume, and an upward force at the top.
Pascal's law states that the force a liquid exerts on a surface is normal to the surface and F=PA.
As the pressure is greater at the bottom of the immersed object then at the top, the liquid pushes the bottom surface upward by a greater force than it pushes the top surface downward. The resultant force is always upward. ehild

 

[vkash]

You get upward force at the bottom of the immersed volume, and an upward force at the top.
Pascal's law states that the force a liquid exerts on a surface is normal to the surface and F=PA.
As the pressure is greater at the bottom of the immersed object then at the top, the liquid pushes the bottom surface upward by a greater force than it pushes the top surface downward. The resultant force is always upward.


ehild

thnank's sir(are u male) for helping me,

 

[ehild]

Can you proceed from here?

ehild

 

[vkash]

Can you proceed from here?

ehild

Actually i have already(before posting) done this question by this method. But I did not understand that is it correct or not. that's why i post it here.

 

[ehild]

Do you understand it now?

Take a block instead of the sphere. The area of the top and bottom sides is A. The pressure at depth d in the oil is
P_t=ρ_oilgd +P₀, so the downward force on the top surface of the block is F_t= A(gρ_oilgd +P₀).

At the bottom of the block, the pressure is that of a column of oil of height d+h/2 and a column of mercury of height h/2. P_b=ρ_oilg(d+h/2)+ ρ_Hgg(h/2)+P₀, so the force Fb =A(ρ_oilg(d+h/2)+ ρ_Hgg(h/2)+P₀)
The resultant is the buoyant force: BF=Ag( ρ_oil(d+h/2)+ ρ_Hg(h/2)-ρ_oild)=Ag(ρ_oil(h/2)+ ρ_Hg(h/2))=g(V/2)(ρ_oil+ ρ_Hg).

ehild