In a u$-$shaped tube with a circular cross$-$section, glycerol $($Density: $$rho oil $=$ $890$ kg$/$m$3)$ and mineral oil $($Density: $$rho glycerol $=1260$ kg$/$m$3)$ are sepa$$rated by a movable membrane as depicted in the figure below.

a$)$ What is the ratio q of the heights glycerol$/$oil when the system is in equilibrium? $(1$P$)$ 

b$)$ Now the membrane is temporarily fixed and the glycerol is filled up until the height of both liquids is equal. After it is released the whole system oscillates. At what distance to the original position is the new equilibrium position? $(2$P$)$ 

c$)$ What is the maximum speed of the membrane during the oscillation set off in b$)?(2$P$)$ Note: The diameter d of the connecting tube is significantly smaller than the heights of the liquids. Assume that the mass of the membrane. membrane is much higher than the total mass of both liquids and that no energy is dissipated during the oscillation.

                       

Transcribed Image Text:

glycerol h, 1 d X ‡d mineral oil D h₂ glycerol h, 1 d X ‡d mineral oil D h₂

Answer rating: 100% (QA)

Solutions Step 1 The question is based on Density and Pressure In a U shaped tube with a circular crosssection glycerol Density oil 890 kgm3 and miner... View the full answer