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

 3936  200 JEE AdvancedJEE Advanced 2019Gravitation Report Error

Solution:

For a particle rotating in the circular orbit of radius r due to the gravitational attraction of inner cloud of mass M,


As constant, then
or
Correspondingly

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