A closed vessel is half-filled with water. Air is pumped out through a hole located near the top of the vessel.

Step-by-step solution

When air is pumped out of the closed vessel, the amount of air above the water surface decreases, leading to a drop in the air pressure. Thus, the pressure at the water surface decreases. The pressure at the bottom of the vessel is given by P_ bottom = P_ surface + g h , where is the density of water, g is the acceleration due to gravity, and h is the height of the water column. Since P_ surface decreases, P_ bottom also decreases. The force exerted by the water on the bottom of the vessel is F = P_ bottom A , wher