A solid cylinder of uniform density of 0.85 g/cm 3 floats in a glass of water ti
ID: 1461055 • 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.
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.
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 The cylinder is replaced with one that has the same density and height, but 1.5× the diameter.
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 A liquid with a density of 1.06 g/cm3 is poured into the glass.
Explanation / Answer
The cylinder is replaced with one that has the same height and diameter, but with density of 0.89 g/cm3.
Since density has decreased now, more of the cyclinder will go float on water
So, X will incraese
The cylinder is replaced with one that has the same density and diameter, but with half the height.
Since height is made smaller
Volume of cylinder will get half and hence mass of cylinder will be halfed
So to balance the weight volume imersed will be half
So No change in X
The cylinder is replaced with one that has the same density and height, but 1.5× the diameter.
No change in X
A liquid with a density of 0.76 g/cm3 is poured into the glass.
average density of liquid will decraese and hence for buoyant force to remain same, more cylinder has to go inside
So X will decrease
More tinted water is added to the glass.
Average density of liquid is not changing
Hence no change in X
A liquid with a density of 1.06 g/cm3 is poured into the glass.
average density of liquid willincraese and hence for buoyant force to remain same, less cylinder has to go inside
So X will increase
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