Physics

Problem

A very large number of small particles form a spherical cloud. Initially they are at rest, have uniform mass density per unit volume,

\rho_0

. The cloud collapses due to gravitation. The particles do not interact with each other in any other way. Initially the radius of cloud is

r_0

. Find the speed of circumference of cloud when radius of cloud is

r(r < r_0)

: a.

V = \sqrt{\frac{2\pi G r_0^2 \rho_0}{3} \left( \frac{r_0}{r} - 1 \right)}

V = \sqrt{\frac{4\pi G r_0^2 \rho_0}{3} \left( \frac{r_0}{r} - 1 \right)}

V = \sqrt{\frac{2\pi G r_0^2 \rho_0}{3} \left( \frac{r_0}{r^2} - 1 \right)}

V = \sqrt{\frac{8\pi G r_0^2 \rho_0}{3} \left( \frac{r_0}{r} - 1 \right)}