Force to balance the force by atmosphere

Question

In the container containing water,let us consider the uppermost surface which is contact with the air. The force by atmosphere $P_oA$ is acting on the upper most surface. If we assume the water to be in equilibrium,an opposite and equal amount of force must be applied on the uppermost surface to counteract $P_oA$. Where does this force arise from? For any point in the bulk of the water,we used to imagine a cylinder and then balance forces. Where will the upward force to balance $P_oA$ come from in this case?

Answer 1

Talking about forces acting on a boundary is a little strange. Forces act on systems, and they can act at a specific location like a boundary. But the boundary itself is not an object, it is just a mathematical surface. It doesn’t have mass and talking about forces balancing on it is suspect at best.

The best that we can do to answer this question is as follows. Since you are already aware that :

For any point in the bulk of the water,we used to imagine a cylinder and then balance forces.

We can simply imagine a cylinder and make the height of the cylinder be a variable, say $h$. Then we just take the limit as $h\to 0$. In that limit the upward force becomes the same as the downward force.