How Does Shell Theorem Apply to Asymmetrical and Perforated Shells?

[zarmewa]

INSIDE SHELL

Not sure if it is done erroneously or blatantly but there is a mammoth difference between

“Force ON the particle” and “Force BETWEEN the particles”

Therefore just suffice it to say that the net force ON the point mass at exact center of the spherical shell is zero but the force BETWEEN shell and point mass is F=GMm/r^2=infinity, because the on center distance of the shell and the point mass coincides id est r = zero

Similarly, would the praxis be amenable to hemispherical shell or quasi cross-section, disorderly holes in the spherical shell and asymmetrical shell?
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Eclectic Eccentric Khattak No.1

GO

 

[Doc Al]

Therefore just suffice it to say that the net force ON the point mass at exact center of the spherical shell is zero but the force BETWEEN shell and point mass is F=GMm/r^2=infinity, because the on center distance of the shell and the point mass coincides id est r = zero

Nope. You cannot treat the mass of the shell as if concentrated at its center when trying to find the force it exerts on a mass within the shell. (And your distinction between force "on" and force "between" doesn't make sense when talking about a point mass within the shell.)

 

[zarmewa]

Is shell theorem applicable to hemispherical shell or quasi cross-section, disorderly holes in the spherical shell and asymmetrical shell?

 

[Doc Al]

Is shell theorem applicable to hemispherical shell or quasi cross-section, disorderly holes in the spherical shell and asymmetrical shell?

No..

 

[pmacias]

VERNMENT SCIENTIST:

Thank you for your question. The Shell Theorem is a fundamental law in physics that states that a spherically symmetric object exerts no net gravitational force on a particle located inside of it. This means that the force ON the particle at the exact center of the spherical shell is zero. However, the force BETWEEN the particle and the shell is not zero and is given by the formula F=GMm/r^2, where G is the gravitational constant, M is the mass of the shell, m is the mass of the particle, and r is the distance between them.

In terms of the praxis, the Shell Theorem applies to all spherically symmetric objects, including hemispherical shells and asymmetrical shells. The theorem does not depend on the shape or size of the shell, as long as it is spherically symmetric. Therefore, the presence of disorderly holes or asymmetrical shapes would not affect the application of the Shell Theorem.

I hope this clarifies any confusion you may have had about the Shell Theorem. If you have further questions or would like to discuss this topic in more detail, please feel free to reach out to me. I am always happy to engage in discussions and help clarify any scientific concepts. Thank you for your interest in this topic.