# Gravitation takes a toll

Classical Mechanics Level pending

A very large number of small particles forms a spherical cloud. Initially, they are at rest, having a uniform mass density per unit volume $$\rho_0$$, 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 collapses entirely?

$t = \sqrt{ \dfrac \pi{96 G \rho_0}} \; .$

The correct ans is of the form $$kt$$ where $$k$$ is a rational number. Report your answer as the value of $$k$$ upto 2 decimals.

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