if we push a wall and no acceleration is produced in it therefore force acting on it should be zero (f=ma)and hence pressure on it mut be zero. but why is it not so???????

It's a common misconception to think that if there's no acceleration, then the force and pressure must be zero. Let's break this down step by step to clarify how forces, pressure, and acceleration interact, especially in the context of pushing against a wall.

Understanding Forces and Pressure

First, let's clarify the relationship between force, mass, and acceleration using Newton's second law, which states:

• F = ma

Here, F represents force, m is mass, and a is acceleration. If you push against a wall and it doesn't move, the acceleration is indeed zero. However, this doesn't mean that the force you exert is zero.

What Happens When You Push a Wall?

When you apply a force to the wall, you're exerting pressure on it. Pressure is defined as force per unit area:

• P = F/A

In this equation, P is pressure, F is the force applied, and A is the area over which the force is distributed. Even if the wall doesn't move, the force you apply is still present, and it creates pressure on the wall.

Why Is There No Acceleration?

The reason the wall doesn't accelerate is that it is also exerting an equal and opposite force back on you, according to Newton's third law of motion:

• For every action, there is an equal and opposite reaction.

So, when you push the wall with a certain force, the wall pushes back with the same amount of force in the opposite direction. This balance of forces results in no net force acting on either you or the wall, which is why there is no acceleration.

Pressure on the Wall

Even though the wall doesn't move, the pressure you exert on it is still significant. For example, if you push against the wall with a force of 100 Newtons and the area of your hand in contact with the wall is 0.1 square meters, the pressure would be:

• P = F/A = 100 N / 0.1 m² = 1000 Pa

This means you are exerting a pressure of 1000 Pascals on the wall, even though it remains stationary. The wall is simply strong enough to withstand that pressure without moving.

Real-World Implications

This principle is crucial in many real-world applications, such as engineering and architecture, where understanding how forces and pressures interact helps in designing structures that can withstand various loads without collapsing.

In summary, while the wall does not accelerate when you push it, the force you apply creates pressure on it. The wall's ability to resist that pressure without moving is what keeps it stable and intact. So, the key takeaway is that force and pressure can exist even in the absence of motion or acceleration.