Consider a spherical gaseous cloud of mass density $\rho(r)$ in free space,where $r$ is the radial distance from its center. The gaseous cloud is made of particles of equal mass $m$ moving in circular orbits about the common center with the same kinetic energy $K$. The force acting on the particles is their mutual gravitational force. If $\rho(r)$ is constant in time,the particle number density $n(r) = \rho(r) / m$ is:
[$G$ is the universal gravitational constant]

• A
  $\frac{K}{\pi r^2 m^2 G}$
• B
  $\frac{K}{6 \pi^2 m^2 G}$
• C
  $\frac{3K}{\pi^2 m^2 G}$
• D
  $\frac{K}{2 \pi r^2 m^2 G}$