Question

On plant Mercury there is a special lake with two layers: dH2O and dHg (liquid mercury). The liquid water layer floats on top of the liquid mercury layer. Let ρH2O and ρHg denote the densities of water and mercury respectively. The gravitational field near the planet’s surface is gy, and the the atmospheric pressure near the surface of the lake P0.

a.Determine an expression in terms of the gi variables for the pressure in the lake as a function of depth all the way to the bottom of the layer of mercury. Graph this function.

b. Suppose an object density ρ is dropped into the lake. Assume ρH2O < ρ < ρHg. What fraction of the object you think will be submerged in the mercury after the object comes to rest in static equilibrium in the limit ρ → ρH2O .What fraction of the object you think will be submerged in the mercury after the object comes to rest in static equilibrium in the limit ρ → ρHg?

c.Determine an expression for ρ in terms of ρH 2O and ρHg that you believe would result in the object being half-submerged in the mercury layer and half-submerged in the water layer?Assume ρH2O < ρ < ρHg

d. Consider the general case where the density of the object is simply the unknown variable p. Determine an expression for the fraction of the object that will be submerged in the mercury when the object comes to rest in static equilibrium?

Answer 1