Its circular surfaces are horizontal. What effect will the following changes, ea
ID: 2092931 • Letter: I
Question
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.
More tinted water is added to the glass.
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 height and diameter, but with density of 0.89 g/cm3.
A liquid with a density of 1.06 g/cm3 is poured into the glass.
A liquid with a density of 0.76 g/cm3 is poured into the glass.
The cylinder is replaced with one that has the same density and height, but 1.5
Explanation / Answer
a) Since the density of the added liquid is more than water it will go below the water and after sometime the water will remain on top and the cylinder will float in the water itself. Hence no change in X b) Now a liquid with lesser density than both water and the cylinder is added. So the cylinder being more denser than the added liquid will stay near the boundary of the liquid and water. Now, think of it this way: initially its just floating in water. Now it has some liquid on top of it as well. So the new liquid i exerting buoyant force. So the amount of buoyant force required from water decreases. Hence the level it outside water decreases. Therefore X decreases. c) Lesser density means lesser weight of the cylinder. This means lesser buoyant force is required to balance its weight. Hence the level X decreases. d) As the cylinder is floating with its circular parts horizontal, the diameter has no affect on the amount of height that is above the water. Hence X doesn't change e) say some b% of the original height is outside initially. Now we are reducing the original height itself. Hence the amount outside, X will decrease. f) Tinted water makes no change in density, so its just the initial scenario. X doesn't change. :)
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