- #1

vcsharp2003

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- Homework Statement
- 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. Mass density is constant in time. If the particle number density is ##n (r ) = \dfrac {\rho (r)} {m}##, then determine it in terms of ## \text {m, K and r}##?

- Relevant Equations
- ##F_g = \dfrac {GMm} {r^2} ##

## F_c = \dfrac {mv^2} {r} ##

## KE = \dfrac {mv^2} {2} ##

This question is very confusing since I don't see

I did consider the following analogy, but it's confusing. The spherical gaseous cloud can be considered like a spherical earth. Then, gravitational force between any outside particle and the gaseous cloud would be like the force between Earth and and an external object. But in our case we have no external particle as the particle is part of the spherical gaseous cloud.

The question clearly states that "

*two*distinct particles that are exerting a gravitational force on each other. Also to complicate matters, a gas is made of many individual particles and I don't know how to determine the gravitational force on a single particle from so many other gaseous particles.*If someone can give me any hint on how to get the gravitational force on a single gas particle from so many other particles then that would help.*I did consider the following analogy, but it's confusing. The spherical gaseous cloud can be considered like a spherical earth. Then, gravitational force between any outside particle and the gaseous cloud would be like the force between Earth and and an external object. But in our case we have no external particle as the particle is part of the spherical gaseous cloud.

The question clearly states that "

*The force acting on the particles is their mutual gravitational force*", but then what should be the big mass M that we should use to mimic a spherical Earth pulling an external object. We know the small mass m is known and its the mass of a particle in circular motion.
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