Three identical glasses are filled to the same height with water. The first glass is filled with water only(Wa). The second glass has an object of volume V and density half that of water floating in it (Wb). The third glass has an object of volume V and density twice that of water on the bottom of it (Wc). All three glasses are sitting on scales. Compare the weight of each of the glasses: Wa, Wb, Wc.
Let
mass of water in Wa = Ma
mass of glass = Mg
a) mass = Ma+Mg
b) mass = Ma + Mg - ρV + ρV = Ma + Mg
c) mass = Ma + Mg + ρV - V = Ma + Mg - (ρ-1)V
To compare the weight of each glass, we need to consider the weight of the water and the weight of the object in the second and third glasses.
Let's start by calculating the weight of each glass:
1. Glass Wa:
Since the first glass contains only water, we can calculate its weight by multiplying the volume of water by the density of water (which is typically around 1 gram per cubic centimeter or 1000 kilograms per cubic meter). Let's assume the volume of water is Vw.
Weight of Wa = Vw * Density of water.
2. Glass Wb:
In the second glass, there is an object floating with a density half that of water. Let's assume the volume of the object is also V.
Weight of Wb = Weight of water (Vw * Density of water) + Weight of object (V * Density of water/2).
3. Glass Wc:
In the third glass, there is an object at the bottom of the glass with a density twice that of water. Again, let's assume the volume of the object is V.
Weight of Wc = Weight of water (Vw * Density of water) + Weight of object (V * Density of water * 2).
Now, to compare the weight of each glass, we need more information about the volume of water (Vw) and the volume of the objects (V). Without those values, we can't determine the exact weights of each glass.