Two stationary particles of masses `M_(1)` and `M_(2)` are 'd' distance apart. A third particle lying on the line joining the particles, experiences no resultant gravitational force. What is the distance of this particle from `M_(1)` ?

Explanation

To solve the problem, we need to find the distance \( x \) from mass \( M_1 \) to the third particle \( m \) such that the gravitational forces acting on \( m \) due to \( M_1 \) and \( M_2 \) are equal and opposite, resulting in no net force.

### Step-by-Step Solution:

1. **Define the Setup**:
- Let the masses be \( M_1 \) and \( M_2 \).
- The distance between \( M_1 \) and \( M_2 \) is \( d \).
- Let the distance from \( M_1 \) to the third particle \( m \) be \( x \).
...