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Two stationary particles of masses M(1) ...

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)` ?

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To solve the problem step by step, we will analyze the gravitational forces acting on the third particle and find its distance from mass \( M_1 \). ### Step 1: Understand the Setup We have two stationary particles with masses \( M_1 \) and \( M_2 \) separated by a distance \( d \). A third particle of mass \( m \) is placed on the line joining \( M_1 \) and \( M_2 \) at a distance \( x \) from \( M_1 \). Therefore, the distance from \( M_2 \) to the third particle will be \( d - x \). **Hint:** Visualize the setup with a diagram to understand the positions of the masses. ### Step 2: Write the Gravitational Forces ...
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