Prove that the centre of mass of two particle divides the line joining the particles in the inverse ratio of their masses.

Explanation

To prove that the center of mass of two particles divides the line joining them in the inverse ratio of their masses, we can follow these steps:

### Step 1: Define the System
Let’s consider two particles with masses \( m_1 \) and \( m_2 \). Assume the position of mass \( m_1 \) is at point \( x_1 \) and the position of mass \( m_2 \) is at point \( x_2 \).

### Step 2: Determine the Position of the Center of Mass
The formula for the center of mass \( x_{cm} \) of a system of particles is given by:

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