Consider an object of mass M that is small enough to be treated as a particle but large enough that a section of mass m can be removed and positioned 3.0 mm from the remaining part. To maximize the magnitude of the gravitational force between the removed section and the remaining part, what should the ratio of m/M be?

Explanation

To solve the problem of maximizing the gravitational force between the removed section of mass \( m \) and the remaining part of mass \( M \), we can follow these steps:

### Step 1: Write the formula for gravitational force
The gravitational force \( F \) between two masses \( m \) and \( M \) separated by a distance \( r \) is given by Newton's law of gravitation:
\[ F = \frac{G \cdot m \cdot M}{r^2} \]
where \( G \) is the gravitational constant and \( r \) is the distance between the two masses.
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