A mass `M` is broken into two parts of masses `m_(1)` and `m_(2)`. How are `m_(1)` and `m_(2)` related so that force of gravitational attraction between the two parts is maximum?

Explanation

To solve the problem of how the masses \( m_1 \) and \( m_2 \) should be related to maximize the gravitational force between them, we can follow these steps:

### Step 1: Define the masses
Let the total mass \( M \) be divided into two parts:
- \( m_1 \)
- \( m_2 \)

Since the total mass is \( M \), we can express \( m_2 \) in terms of \( m_1 \):
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