A solid cylinder of uniform density of 0.85 g/cm 3 floats in a glass of water ti
ID: 1550979 • Letter: A
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.
OPTIONS FOR ANSWERS: Increase, decrease, no change
1.The cylinder is replaced with one that has the same height and diameter, but with density of 0.89 g/cm3.
2.A liquid with a density of 1.06 g/cm3 is poured into the glass.
3.The cylinder is replaced with one that has the same density and diameter, but with half the height.
4.A liquid with a density of 0.76 g/cm3 is poured into the glass.
5. The cylinder is replaced with one that has the same density and height, but 1.5× the diameter.
6. More tinted water is added to the glass.
Explanation / Answer
1. Decrease
as the density of cylinder increase for the same diameter and height (same volume) , the mass of cylinder increases since
Mass = density x Volume .
as the mass of cylinder increase , it will displace more liquid and hence its height above water will decrease.
2)
No change , Since the liquid added do not mix with water
3)
Decrease
with same diameter and half height , the Volume of cylinder decrease . density remain same
hence mass = density x Volume decrease
although the cylinder is pushed some distance out of water but the height overall above water decrease.
4)
Increase.
5)
No change
6)
No change
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