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 height, but 1.5 x 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 1.06 g/cm^3 is poured into the glass. More tinted water is added to the glass. A liquid with a density of 0.76 g/cm^3 is poured into the glass. The cylinder is replaced with one that has the same height and diameter, but with density of 0.89 g/cm^3.

Explanation / Answer

As at equilibrium weight of block will be balanced by buoyancy force on the block. And buoyancy force is density of liquid multiplied by volume displaced of the liquid.

Case 1. As area increases hence to displace same volume less height of volume will be inside liquid hence x increases in first case.

Case 2. As height is halved x will decrease as volume displaced has to be same for equilibrium.

Case 3. As liquid of more density is added hence liquid displaced has to be lesser hence x will increase.

Case 4. More same liquid is added, for equilibrium volume displaced has to be same, hence no change in x.

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