The gravitational potential at a point outside the solid sphere of radius "R" and at a distance of "r" will be :

Options

A. linearly dependent on r
B. proportional to `(1)/(r)`
C. proportional to `r^(2)`
D. same everywhere

Answer

To find the gravitational potential at a point outside a solid sphere of radius \( R \) and at a distance \( r \) from the center of the sphere, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Gravitational Potential**:
The gravitational potential \( V \) at a distance \( r \) from a mass \( M \) is given by the formula:
\[ V = -\frac{G M}{r} \]
where \( G \) is the gravitational constant.

2. **Identifying the Mass of the Sphere**:
For a solid sphere of radius \( R \) and mass \( M \), when we are outside the sphere (i.e., at a distance \( r \) such that \( r > R \)), the sphere can be treated as if all its mass were concentrated at its center.

3. **Applying the Formula**:
Since we are considering a point outside the sphere, we can substitute \( M \) (the mass of the sphere) into the gravitational potential formula:
\[ V = -\frac{G M}{r} \]

4. **Conclusion**:
Thus, the gravitational potential at a point outside the solid sphere at a distance \( r \) from its center is:
\[ V = -\frac{G M}{r} \]
This shows that the gravitational potential depends inversely on the distance \( r \).

### Final Answer:
The gravitational potential at a point outside the solid sphere of radius \( R \) and at a distance \( r \) is given by:
\[ V = -\frac{G M}{r} \]