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Gravitational force exerted by half of a ball of uniform density

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Compute the gravitational force exerted by half of a ball of radius R of uniform density rho on the other half.

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Solution Summary

I give a detailed solution using Gauss' law to find the gravitational force exerted.

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The gravitational field of half of a ball of radius R of density rho is an extremely complex function of the position. We can nevertheless compute the force exerted on the other half of the ball without having to do complex computations as follows.

The key observation is that we can compute the force exerted on a region by integrating the total force on each ...

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