A solid cylinder of uniform density of 0.85 g/cm^3 floats in a glass of water ti

Question

A solid cylinder of uniform density of 0.85 g/cm^3 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. 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 1.5x the diameter. Some of the water is removed from the glass. The cylinder is replaced with one that has the same height and diameter, but with density of 0.83 g/cm^3. A liquid with a density of 1.06 g/cm^3 is poured into the glass. A liquid with a density of 0.76 g/cm^3 is poured into the glass.

Explanation / Answer

1. No change because height of cyclinder doesn't effect, and other factors are remaining same.

2. Increases because the diameter is bigger. The overall percentage of the cylinder underwater and above water is still the same because the density is same, but since the diameter is bigger, more would be height of upper surface.

3. No change as density is remaining same.

4. Decrease because the density causes it to sink a little more, so it would be more submerged and less would be the height of the upper surface.

5. Increase because water's density is about 1.00 g/cm3, and the liquid that is poured has a higher density, means that it forms a new layer which raises the cylinder.

6. Decreases because the liquid added has a lower density than water and the cylinder, so that means that that liquid will be on the top layer, pushing the cylinder down.

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