Answer
In situation 1, the density of the red liquid is less than the density of the gray liquid.
In situation 3, the density of the red liquid is equal to the density of the gray liquid.
In situation 4, the density of the red liquid is greater than the density of the gray liquid.
Work Step by Step
In part (a), we found that situation 2 can not be in static equilibrium.
In situation 1, the pressure at the level of the bottom dotted line is the same on the left and on the right. Thus the weight of the red liquid above the dotted line is equal to the weight of the gray liquid above the dotted line. Since there is more red liquid, the density of the red liquid is less than the density of the gray liquid.
In situation 3, the pressure at the level of the bottom dotted line is the same on the left and on the right. Thus the weight of the red liquid above the dotted line is equal to the weight of the gray liquid above the dotted line. Since there is an equal amount of red liquid and gray liquid above the dotted line, the density of the red liquid is equal to the density of the gray liquid.
In situation 4, the pressure at the level of the bottom dotted line is the same on the left and on the right. Thus the weight of the red liquid above the dotted line is equal to the weight of the gray liquid above the dotted line. Since there is less red liquid, the density of the red liquid is greater than the density of the gray liquid.
