What is the relationship between pressure and force inside a spherical object?

[PSN03]

Homework Statement

A uniform sphere has a mass M and radius R. Find the pressure p inside the sphere caused by gravitational compression, as a function of distance r from its centre.

Relevant Equations

Pressure*Area=Force
Force=GM1M2/R²

So I already have a solution available to this problem and the link for the solution is:


I have understood everything in the video except the part where they are equating the force
dF=GM/r²*dm
According to my reasoning the inner part of the sphere (the part below the dm element we have taken) will have mass M and can be treated as a point sized object. This object will have a field E=GM/r² at a distance of r from the centre.
The dm element that we are taking into consideration is a spherical shell. It's centre of mass shoul coincide with the centre of mass of the sphere, hence there shouldn't be any distance between the two bodies to apply Newton's law of gravitation.
So my doubt it howare they applying the formula to dm mass even though it isn't point sized and distributed over a surface.

 

[TSny]

I have understood everything in the video except the part where they are equating the force
dF=GM/r²*dm

This expression for the gravitational force on the spherical shell can be misleading. The net gravitational force on the shell is zero as you can easily see by considering diametrically opposite elements of mass in the shell:

 

[PSN03]

This expression for the gravitational force on the spherical shell can be misleading. The net gravitational force on the shell is zero as you can easily see by considering diametrically opposite elements of mass in the shell:

Yes you have a point there. Then how is the man in video applying it ?
Moreover we should consider the centre of mass of the elemental sphere while writing the above expression...right?

 

[TSny]

I have understood everything in the video except the part where they are equating the force
dF=GM/r²*dm

This expression for the gravitational force on the spherical shell isn't really correct. The net gravitational force on the shell is zero as you can easily see by considering diametrically opposite elements of equal mass in the shell:

The two gravitational forces shown add to zero. Thus, the net gravitational force on the entire shell is zero.

It is less confusing if you consider just one element of mass of the shell as shown below:

Consider the balance of gravitational force and pressure force on this one element.

 

[PSN03]

This expression for the gravitational force on the spherical shell isn't really correct. The net gravitational force on the shell is zero as you can easily see by considering diametrically opposite elements of equal mass in the shell:
View attachment 267968

The two gravitational forces shown add to zero. Thus, the net gravitational force on the entire shell is zero.

It is less confusing if you consider just one element of mass of the shell as shown below:

View attachment 267971

Consider the balance of gravitational force and pressure force on this one element.

How to proceed further after taking one element of this mass shell?

 

[PSN03]

This expression for the gravitational force on the spherical shell isn't really correct. The net gravitational force on the shell is zero as you can easily see by considering diametrically opposite elements of equal mass in the shell:
View attachment 267968

The two gravitational forces shown add to zero. Thus, the net gravitational force on the entire shell is zero.

It is less confusing if you consider just one element of mass of the shell as shown below:

View attachment 267971

Consider the balance of gravitational force and pressure force on this one element.

Hey @TSny I have got what you were trying to tell. Also I found a similar video solution to this problem but it's in my regional language so I can't upload it but I have got the solution.
Thanks for your help.
Good day and stay safe