0.140- cube of ice (frozen water) is floating in glycerine. The gylcerine is in a tall cylinder that has inside radius 3.30 . The level of the glycerine is well below the top of the cylinder.If the ice completely melts, by what distance does the height of liquid in the cylinder change?Does the level of liquid rise or fall? That is, is the surface of the water above or below the original level of the gylcerine before the ice melted?
To determine the change in the liquid's height in the cylinder when the ice melts and whether the level rises or falls, we need to consider the principles of buoyancy and Archimedes' principle.
First, let's calculate the volume of the ice cube. Since the density of water is approximately 1 gram per cubic centimeter, the mass of the ice cube is:
Mass = Density × Volume
Mass = 1 g/cm³ × (0.140 cm)³
Mass = 0.00194 kg
Since the density of glycerine is approximately 1.26 grams per cubic centimeter, the volume of liquid displaced by the ice cube is:
Volume Displaced = Mass of Ice Cube / Density of Glycerine
Volume Displaced = 0.00194 kg / 1.26 g/cm³
Volume Displaced = 0.001540 cm³
Next, we can calculate the change in liquid height using the formula:
Change in Height = Volume Displaced / (π × (inside radius)²)
Change in Height = 0.001540 cm³ / (π × (3.30 cm)²)
Change in Height ≈ 0.01472 cm (rounded to four decimal places)
Now let's determine whether the level of the liquid rises or falls. Based on the calculation above, we can conclude that the level of the liquid rises. This is because the volume of water resulting from the melted ice is greater than the volume of the ice itself. Thus, the surface of the water will be above the original level of the glycerine before the ice melted.