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

Options

A. `(k)/(2pi r^2 m^2 G)`
B. `(k )/(pi r^2m^2 G)`
C. `(3k)/(pi r^2 m^2 G)`
D. `(k )/(6pi r^2 m^2 G)`