State and prove Archimedes principle. from Physics Mechanical Properties of Fluids Class 11 Manipur Board

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State and prove Archimedes principle.

Archimedes principle: When a body is immersed partially or wholly in a liquid, its weight appears to be reduced and loss of weight is equal to the weight of liquid displaced by the body.

Proof: Consider a body of height h and area of cross-section A placed in liquid of density σ at a depth x below the free surface.

Let ρ be density of the body.

Now the pressure at the upper face of the body is,

where,  Pis atmospheric pressure.

Pressure at the lower face of the body is,

Therefore downward thrust on  upper face of the body is,

and upward thrust on lower face of body is,

Since P> P1  therefore F> F

Body will experience the net force F- Fin upward direction known as upward thrust.

where, V is volume of body

= Weight of liquid displaced by body.

Now, the  body experiences two forces: weight of the body itself and upward thrust.

i.e. Apparent weight is less than the actual weight by amount equal to weight of liquid displaced by body.

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What is hydrostatics?

Hydrostatics is the branch of fluid mechanics that studies incompressible fluids at rest. The study of fluids at rest or objects placed at rest in fluids is hydrostatics.
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What is hydrodynamics?

Hydrodynamics is the branch of science that studies about the force exerted by the fluids or acting on the fluids.
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Do intermolecular or inter-atomic forces follow inverse square law?

No. Intermolecular and inter-atomic forces do not obey the inverse square law.
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Why solids have definite shape while liquids do not have definite shape?

Solids: Intermolecular forces are very strong and thermal agitations are not sufficiently strong to separate the molecules from their mean position. Solids are rigid and hence they have definite shapes.
Liquids: In liquids intermolecular forces are not sufficiently strong to hold the molecules at definite sites, as a result they move freely within the bulk of liquid, therefore, do not possess definite shapes. Liquids take the same shape as that of the container.
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What is fluid?

Any material that can flow is a fluid. Liquids and gases are examples of fluid.

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