A classical mechanics problem by Jason Hu

Classical Mechanics Level pending

A very large number of small particles forms a spherical cloud. Initially they are at rest, have uniform mass density per unit volume ρ, and occupy a region of radius r. The cloud collapses due to gravitation; the particles do not interact with each other in any other way. How much time passes until the cloud collapses fully? The time is expressed as x/sqrt(Gρ), where G is the universal gravitational constant. Find 10000x.

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