If a perfect sphere resting on a perfect surface makes contact at a single point, does its mass exert infinite pressure?
by 
Mawgan
ANSWERS: 4
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No. Geometry does not supersede how physics works. You must have infinite force to achieve infinite pressure.
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Yes, it does. Pressure is measured in force divided by area. The force here is constant but as the surface area approaches zero the pressure increases to infinity. The result is meaningless since the inifinite pressure is exerted over an infinitesimally small area. Using idealized models you can come up with all sorts of meaningless results. It would probably be more appropriate to say that the pressure at that point is undefined.
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No, because the amount pressure exerted through this contact will be directly related to the mass of the sphere and the amount of the gravitational field, if any, the sphere and the surface it's resting on are in. In your question, you stated that the sphere is RESTING on the surface without any outside force acting on it. So, even given that this would be an experiment performed at sea level here on Earth, you would only be able to achieve infinite pressure if you were somehow able to apply infinite force to the sphere.
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Only if both sphere and surface are infinitely perfect and infinitely hard. So in the land of mathematical conjecture, where pure dimensionless points are real, Yes. But in the real world, where spheres and surfaces have to be constructed out of atoms which have a finite size and deflect under pressure, the contact area will always have a finite size and the pressure will therefore be less than infinite.
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