Calculate the self-gravitational potential energy of matter forming a. a thin uniform shell of mass `M` and radius `R`, b. a uniform sphere of mass `m` and radius `R`.

Explanation

To solve the problem of calculating the self-gravitational potential energy for both a thin uniform shell and a uniform sphere, we will follow these steps:

### Part A: Self-Gravitational Potential Energy of a Thin Uniform Shell

1. **Understanding the Shell**: We consider a thin spherical shell of mass \( M \) and radius \( R \).

2. **Gravitational Potential Due to the Shell**: The gravitational potential \( V \) at the surface of the shell (or inside it) is given by:
\[
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