Observe the situation depicted in the figure. The wall is smooth,...

Consider the system comprising both blocks A and B.

The external forces acting on this system in the vertical direction are their respective weights, $m_A g$ and $m_B g$, which act downwards.

Since the wall is smooth, it cannot exert any vertical frictional force on block A. It only provides a horizontal normal reaction.

The applied force $F$ is purely horizontal and provides no vertical component.

Therefore, there is no external upward force to balance the total downward gravitational force $(m_A + m_B)g$.

Since the net vertical force on the system is non-zero, the system cannot remain in equilibrium and will accelerate downwards.