The mechanical and optical properties of a small spherical particle may be assumed to be independent of the temperature and pressure. Its density and optical properties are the same as those of water at 30C. The particle is suspended inside a vertical column of water across which there is a roughly uniform temperature gradient. In case A the top of the water column is maintained at 50C, the bottom at 10C. In case B the temperatures are reversed. The particle may experience four forces acting on it: (i) a gravitational (buoyancy) force, (ii) a van der Waals force, (iii) a force due to the flow of the liquid, and (iv) a force due to the Brownian motion (molecular collisions) of the water molecules. In each case, in which directions do these four forces initially act if the particle is placed at the center of the column? If your answer is "there is no force", state whether the 'equilibrium' is stable or unstable ('metastable'), i.e., whether the particle will return to the center if it is displaced from it by a small amount (up or down), or whether it will continue to move away from the center. Explain scientifically how you arrive at each conclusion. Make sketches of the fluid circulation patterns if this helps you explain your analysis