Question

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

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.

(No change, increase, decrease)

More tinted water is added to the glass.
The cylinder is replaced with one that has the same height and diameter, but with density of 0.83 g/cm³.
A liquid with a density of 0.76 g/cm³ is poured into 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 diameter, but with half the height.
The cylinder is replaced with one that has the same density and height, but 1.5× the diameter.

Answer 1

More tinted water is added to the glass. NO CHANGE
The cylinder is replaced with one that has the same height and diameter, but with density of 0.83 g/cm³. INCREASE
A liquid with a density of 0.76 g/cm³ is poured into the glass. INCREASE
A liquid with a density of 1.06 g/cm³ is poured into the glass. NO CHANGE
The cylinder is replaced with one that has the same density and diameter, but with half the height. NO CHANGE
The cylinder is replaced with one that has the same density and height, but 1.5× the diameter. DECREASE