the order of liquids from bottom to top is Mercury - Water - Oil
Explanation:
In general, when several substances are mixed we can have two cases, that the substances dissolve some enter and that the substances have not been miscible (insoluble) this is our case, the three substances do not dissolve.
Therefore they must be deposited according to the principle of Archimedes,
B -W = 0
if the thrust (B) of the liquid is greater than the weight of the upper body, the body floats and if less, the body sinks.
B = ρ_{liquid1} g V_{liquid2}
W = m_{liquid2} g
substance densities are tabulated
ρ_{oil} = 750 to 950 kg / m3
ρ_ water = 1.00 10³ kg / m³
ρ_ Hg = 13.6 10³ kg / m #
The thrust created by the mercury is
B_Hg = ρ_Hg g V_ Liquid2
B_Hg = 13.6 10³ 9.8 V
B _Hg = 133.3 10³ V
The push of the water
B_water = 1 10³ 9.8 V
B_water = 9.8 10³ V
The oil density, let us use ρ_oil = 0.75 10³ kg / m³
B_ oil = 0.750 10³ 9.8 V
B _ oil = 7.35 10³ V
let's find the volumes of the bodies
Mercury
ρ = m / V
V_hg = m /ρ_Hg
V_Hg = 20 10⁻³/ 13.6 10³
V_Hg = 1.47 10⁻⁶ m³
Water
V_water = 50 10⁻³ L
we reduce from liter to m³ 1000 l = 1 m³
V_water = 50 10⁻⁶ m³
Oil
V_oil = 25 10⁻³ l
V_oil = 25 10⁻⁶ m³
Let's look for the push for every two substances
The mercury in the bottom and upper sustabce the water and oil
B_hg = 133.3 10³ (V_water + V_oil)
B = Hg = 133.3 10³ (50 + 25) 10⁻⁶
B = 10 N
the weight of substance on mercury is
W = W_water + W_oil
W = ρ_water g V_water + ρ_oil g V_oil
W = g (ρ_water V_water + ρ_oil V_oil)
W = 9.8 (1 10³ 50 10⁻⁶ + 0.75 10³ 25 10⁻⁶)
W = 9.8 68.75 10⁻³
W = 6.7 10⁻¹ N
We can be that the weight of this substance in less than the push created by the mercury therefore they float.
In resume the mercury is the substance that will be at the bottom of the cylinder.
Let's repeat the calculation for water and oil.
Suppose the water is below
B₂ = ρ_water g V_oil
B₂ = 1 10³ 9.8 25 10⁻⁶
B₂ = 245 10⁻³ N
B₂ = 2.5 10⁻¹ N
The weight of the oil
W = ρ_oil g V_oil
W = 0.750 10³ 9.8 25 10⁻⁶
W = 183.75 10⁻³
W = 1.8 10⁻¹ N
we see that the thrust of the water is greater than the weight of the oil therefore the oil floats in the water
In summary the order of liquids from bottom to top is
Mercury - Water - Oil
