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.

For the following, increase, decrease, or no change:

The cylinder is replaced with one that has the same density and diameter, but with 1.5× the height.
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 height and diameter, but with density of 0.83 g/cm³.
A liquid with a density of 1.06 g/cm³ is poured into the glass.
A liquid with a density of 0.76 g/cm³ is poured into the glass.
More tinted water is added to the glass.

Answer 1

1. No change

The increase in the weight of the cylinder due to increased height is counterbalanced by the increased buoyant force due to increase of water displaced by the submerged portion of cylinder. So, no change in X

2. No change

Same reasoning as in 1

3. Increase

As density falls, the buoyant force pushes up the lighter cylinder.

4. No change.

The heavier liquid settles at the bottom. So , it doesn't interfere with the buoyant force acting on cylinder

5. Decrease

The heavier cylinder submerges in the lighter liquid due to insufficient buoyant force.

6. No change

Tinting water had no effect whatsoever in the density of water.