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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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  • $\begingroup$ It is zero, although this has no bearing on real life. A sphere is a mathematical idealization, not a real-world object. $\endgroup$ – user296602 Feb 21 at 18:29
  • $\begingroup$ Because spheres in real life deform and are not perfect spheres to begin with. $\endgroup$ – Matthew Liu Feb 21 at 18:30
  • $\begingroup$ So you mean, if we have perfectly shaped solid sphere ball, we will get zero area between wall and object... $\endgroup$ – Tarlan Ahad Feb 21 at 18:32
  • $\begingroup$ Yes, but it's meaningless to talk about a perfectly spherical ball in the real world. Something made up of atoms won't be spherical, and if you zoom in far enough then the boundary isn't a meaningful distinction. $\endgroup$ – user296602 Feb 21 at 18:34
  • $\begingroup$ Thanks for a great explanation. $\endgroup$ – Tarlan Ahad Feb 21 at 18:43
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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.

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