(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Consider a cloud of gaseous hydrogen contracting under gravity to form a star. The cloud is assumed to be spherical of volume [tex]\Omega[/tex] and mass [tex]M[/tex] distributed uniformly.

Show that the gravitational presure of the cloud is

P([tex]\Omega[/tex])=-(1/5)(4pi/3)^(1/3)GM^2/[tex]\Omega[/tex]^2

2. Relevant equations

Gravitational Potential Energy of a sphere is given by -(3/5)GM^2/R.

This means that a Gravitational force is acting on the particles of the sphere to keep the sphere intact. This force is given by

F=-grad(P.E.)

F=-(3/5)GM^2/R^2

This force is acting on the entire surfacr of the sphere whose area is A= 4pi R^2

Therefore gravitational pressure is F/A

P([tex]\Omega[/tex])=-[(3/5)GM^2/R^2]/4pi R^2

on getting rid of R I get the required result.

3. The attempt at a solution

Where's the problem. Well this was a delebrate derivation. First of all I don't clearly understand what does gravitational pressure mean(ie. is it calculated form F/A or there are other ways of calculating it). Second, the area that I have considered is the surface area of the sphere. Well the Gravitational force is acting in the inside of the sphere also. Moreover gravitational pressure should be a function of r(the radial distance from the core) instead of R as common sense tells that gravitational pressure should be maximum at the core and minimum at the surface of the sphere.

Please help me remove my doubts.

There further parts of the question which I wish to ask later..

Thanks.

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# Homework Help: Gravitational Pressure

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