Answer:
Change 1: No change in x.
Change 2: Increase in x.
Change 3: Decrease in x.
Change 4: Decrease in x.
Change 5: Decrease in x.
Change 6: Decrease in x.
Change 7: No change in x.
Step-by-step explanation:
Change 1: The cylinder is replaced with one that has the same density and diameter, but with 1.5 times the height.
Since the density and diameter remain the same, the buoyant force remains constant. The volume of the cylinder increases by 1.5 times, but the submerged volume (the volume of the cylinder that is displaced by the water) also increases by 1.5 times. Therefore, the height of the upper surface above the water (x) will remain the same.
Effect: No change in x.
Change 2: A liquid with a density of 1.06 g/cm3 is poured into the glass.
Introducing a denser liquid below the cylinder will increase the buoyant force acting on the cylinder. This is because the denser liquid exerts a greater upward force on the cylinder, effectively pushing the cylinder higher in the water. Consequently, the height of the upper surface above the water (x) will increase.
Effect: Increase in x.
Change 3: The cylinder is replaced with one that has the same height and diameter, but with a density of 0.83 g/cm3.
Reducing the density of the cylinder will decrease the buoyant force acting on the cylinder. This is because the less dense cylinder displaces less water, resulting in a smaller upward force from the water. As a result, the cylinder will sink lower in the water, and the height of the upper surface above the water (x) will decrease.
Effect: Decrease in x.
Change 4: A liquid with a density of 0.76 g/cm3 is poured into the glass.
Introducing a less dense liquid below the cylinder will decrease the buoyant force acting on the cylinder. Similar to Change 3, the less dense liquid exerts a weaker upward force on the cylinder, causing it to sink lower in the water. Therefore, the height of the upper surface above the water (x) will decrease.
Effect: Decrease in x.
Change 5: Some of the water is removed from the glass.
Removing some of the water will decrease the submerged volume of the cylinder. Since the cylinder's volume remains the same, a smaller portion of it will be displaced by the water. This will cause the cylinder to sink lower in the water, and the height of the upper surface above the water (x) will decrease.
Effect: Decrease in x.
Change 6: The cylinder is replaced with one that has the same density and height, but 1.5 times the diameter.
Increasing the diameter of the cylinder will increase its volume and, consequently, the submerged volume. The buoyant force will also increase due to the larger volume of water being displaced. However, the increase in buoyant force will not be proportional to the increase in volume, as the upward force from the water depends on the cross-sectional area of the cylinder, which increases only with the square of the diameter. As a result, the buoyant force will not increase enough to offset the increased submerged volume, and the cylinder will sink lower in the water. Therefore, the height of the upper surface above the water (x) will decrease.
Effect: Decrease in x.
Change 7: More tinted water is added to the glass.
Adding more tinted water, which has the same density as the initial water, will not affect the buoyant force acting on the cylinder. The cylinder will remain submerged in the same volume of water, and its height above the water will remain unchanged.
Effect: No change in x.