A solid cylinder of uniform density of 0.85 g/cm3 floats in

[Spartan73]

Homework Statement

A solid cylinder of uniform density of 0.85 g/cm3 floats in a glass of water tinted light blue by food coloring.
https://s1.lite.msu.edu/res/msu/kashy/physicsLib02/32_Fluids1_Pascal_Arch/graphics/archimedes.gif
Its circular surfaces are horizontal. What effect will the following changes, each made to the initial system, have on X, the height of the upper surface above the water? The liquids added do not mix with the water, and the cylinder never hits the bottom. The cylinder is replaced with one that has the same height and diameter, but with density of 0.83 g/cm3.
Some of the water is removed from the glass.
A liquid with a density of 1.06 g/cm3 is poured into the glass.
The cylinder is replaced with one that has the same density and height, but 1.5× the diameter.
The cylinder is replaced with one that has the same density and diameter, but with half the height.
A liquid with a density of 0.76 g/cm3 is poured into the glass.

Homework Equations

The Attempt at a Solution

I
N
I
N
N
D
[/B]

 

[drvrm]

solid cylinder of uniform density of 0.85 g/cm3 floats in a glass of water tinted light blue by food coloring.

try to work out and show on template so that we can contribute

 

[haruspex]

Homework Statement

A solid cylinder of uniform density of 0.85 g/cm3 floats in a glass of water tinted light blue by food coloring.
https://s1.lite.msu.edu/res/msu/kashy/physicsLib02/32_Fluids1_Pascal_Arch/graphics/archimedes.gif
Its circular surfaces are horizontal. What effect will the following changes, each made to the initial system, have on X, the height of the upper surface above the water? The liquids added do not mix with the water, and the cylinder never hits the bottom. The cylinder is replaced with one that has the same height and diameter, but with density of 0.83 g/cm3.
Some of the water is removed from the glass.
A liquid with a density of 1.06 g/cm3 is poured into the glass.
The cylinder is replaced with one that has the same density and height, but 1.5× the diameter.
The cylinder is replaced with one that has the same density and diameter, but with half the height.
A liquid with a density of 0.76 g/cm3 is poured into the glass.

Homework Equations

The Attempt at a Solution

I
N
I
N
N
D[/B]

For the third one, draw a diagram showing the two liquids and the cylinder.
For the fifth one, please explain your reason for saying no change.
For the last one, note that X is defined as the height of the top of the cylinder above the water.