Area of touching part of Sphere to the wall.

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I believe that it has a very simple explanation but one question stuck in my mind. What is the area between sphere and wall when it touches to it.

If it is zero, why it is not occurring in real life?

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When you say "sphere" you specify a mathematical construct. The sphere is tangent to the wall and the area of contact is zero. That presumes that the sphere is completely rigid. For many purposes that is a good approximation, but all materials deform if a pressure is applied. That deformation will force the thing you called a sphere to no longer be a sphere. It will have a flat spot at the wall contact. Given the mass, radius, and elastic modulus of the "sphere" it is a reasonable mechanical engineering calculation to approximately find the deformation and the area of contact.