The weight of an aero plane flying in air is balanced by

The correct answer is: Force due to the pressure difference between the upper and lower surfaces of the wings, created by different air speeds on the surface.

Step-by-Step Explanation:

1. Understanding the Wing Design (Aerofoil):
The wings of an airplane are designed with a special cross-sectional shape called an aerofoil (or airfoil). The upper surface of the wing is curved outward (convex), while the lower surface is relatively flat.

2. Airflow and Bernoulli's Principle:
As the airplane moves forward, air streams past the wings. Due to the curvature of the upper surface, the air traveling over the top of the wing has to travel a longer path and move faster than the air passing underneath the flat bottom of the wing.
According to Bernoulli's principle, for a streamline flow of an ideal fluid (or gas like air), the sum of pressure energy, kinetic energy, and potential energy per unit volume remains constant. Mathematically, this is expressed as:

$P+\frac{1}{2}$

Since the change in height ($h$) across the thickness of a wing is negligible, we can simplify this relation to:

$P+\frac{1}{2}$

Here, $P$ represents the static pressure of air, $\rho$ is the density of air, and $v$ is the speed of the air. This equation implies that where the velocity of the air is high, the pressure is low, and vice versa.

3. Creation of Dynamic Lift:
Since the air speed over the upper surface ($v_{\text{upper}}$) is greater than the air speed under the lower surface ($v_{\text{lower}}$), the pressure on the upper surface ($P_{\text{upper}}$) becomes lower than the pressure on the lower surface ($P_{\text{lower}}$):

$P_{\text{lower}}>P_{\text{upper}}$

This pressure difference ($\Delta P=P_{\text{lower}}-P_{\text{upper}}$) acts over the area ($A$) of the wings, creating an upward force called dynamic lift:

$\mathrm{Lift}=\Delta P\times A$

4. Balancing the Airplane's Weight:
In steady, level flight, this upward lift force is precisely equal and opposite to the downward gravitational pull (weight) of the airplane, keeping it suspended and balanced in the air.