Spheres of the same material and same radius `r` are touching each other. Show that gravitational force between them is directly proportional to `r^(4)`.

Explanation

To show that the gravitational force between two spheres of the same material and radius \( r \) is directly proportional to \( r^4 \), we can follow these steps:

### Step-by-Step Solution:

1. **Define the Mass of Each Sphere**:
Since the spheres are made of the same material and have the same radius \( r \), we can express their mass \( m \) in terms of density \( \rho \) and volume. The volume \( V \) of a sphere is given by:
\[
V = \frac{4}{3} \pi r^3
...