Find the gravitational potential due to a spherical shell of mass `M` and radius `R` at `r lt R` and `r gt R`, where `r` is the distance from the centre of the shell.

Explanation

To find the gravitational potential \( V \) due to a spherical shell of mass \( M \) and radius \( R \), we will consider two cases: when the distance \( r \) from the center of the shell is less than \( R \) (i.e., \( r < R \)) and when \( r \) is greater than \( R \) (i.e., \( r > R \)).

### Step 1: Gravitational Potential Inside the Shell (\( r < R \))

1. **Understanding the Shell Theorem**: According to the Shell Theorem, a uniform spherical shell of mass exerts no gravitational force on any object located inside it. This means that the gravitational field \( g \) inside the shell is zero.

2. **Finding the Gravitational Potential**: The gravitational potential \( V \) is related to the gravitational field \( g \) by the equation:
\[
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