A very large number of small particles forms a spherical cloud. Initial they are at rest, have uniform mass density per unit volume ρ 0 and occupy a region of radius r 0 . The cloud collapses due

Question

A very large number of small particles forms a spherical cloud. Initial they are at rest, have uniform mass density per unit volume ρ 0 ​ and occupy a region of radius r 0 ​ . 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 collapse fully?

TestHub · Accepted Answer

​ a = r 2 GM 0 ​ ​ [ M 0 ​ ⇒ ρ 0 ​ 3 4 ​ π r 0 3 ​ ] ​ ∫ 0 v ​ vdv ⇒ − GM 0 ​ ∫ r 0 ​ r ​ r 2 dr ​ ​ 2 v 2 ​ = + GM 0 ​ [ r 1 ​ − r 0 ​ 1 ​ ] ​ v ⇒ 2 GM 0 ​ ( rr 0 ​ r 0 ​ − r ​ ) ​ ​ Put v = dt dr ​ and Integrate. ​

Physics - Gravitation Question with Solution | TestHub

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