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Sagot :
Answer:
see that for the same pressure the displaced height in each cylinder is different because its diameter is different. Pascal's principle
Explanation:
The pressure on a system is given by the relations
P = ρ g h
P = F / A
where ρ is the density of the liquid, h the height and A the area
The expressions above we see that if for the same height the pressure is the same regardless of the shape of the cylinder.
With the second expression we see that if the system has a different area, the pressure is
P = [tex]\frac{F_{1} }{A_{1} } = \frac{F_{2} }{A_{2} }[/tex]
where we use subscript 1 for one body and subscript 2 for the other body
F₁ = [tex]\frac{A_{1} }{A_{2} } F_{2}[/tex]
The cylinder displacement is
V = A h
where V is the volume and h the height, in general the liquids are incompressible therefore the displaced volume is constant in the two bodies
V = A₁ h₁ = A₂ h₂
[tex]\frac{A_{1} }{A_2} = \frac{h_2}{h_1}[/tex]
we substitute
F₁ = [tex]\frac{h_2}{h_1}[/tex] F2
From here we see that for the same pressure the displaced height in each cylinder is different because its diameter is different.
If the diameter is the same, the offset height is the same
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