JEE Advanced 2019 Physics question
Consider a spherical gaseous cloud of mass density 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 is constant in time, the particle number density is [ is universal gravitational constant]
Answer: (A)
Solution
For a particle in a circular orbit of radius , gravity due to the mass enclosed within provides the centripetal force: . Differentiating,
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