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.

The cylinder is replaced with one that has the same density and height, but 1.5× the diameter.
Increase Decrease No change  The cylinder is replaced with one that has the same density and diameter, but with half the height.
Increase Decrease No change  A liquid with a density of 1.06 g/cm³ is poured into the glass.
Increase Decrease No change  A liquid with a density of 0.76 g/cm³ is poured into the glass.
Increase Decrease No change  More tinted water is added to the glass.
Increase Decrease No change  The cylinder is replaced with one that has the same height and diameter, but with density of 0.89 g/cm³.

Answer 1

(a) No change,

Bouyant force depends only on height of cylinder, not area

(b) Decreases,

X will Decreases to half

(c) No change,

Heigher densed liquid lie down to the glass under water

(d) Decreases,

Inorder to equate bouyant force to weight of solid cylinder more volume of low density liquid have to be raised to the level of cylinder, so X decreases

(e) No change

(f) Decreases

Density of cylinder increases, so weight increases, so water level rises, so X decreases