Two particles of masses `2 kg` and `4 kg` are approaching towards each other with ccelerations `1m//s^(2)` and `2m//s^(2)`, respectively, on a smooth horizontal suface. Then find the acceleration of centre of mass of the system and direction of acceleration of CM.

Explanation

To find the acceleration of the center of mass (CM) of the system consisting of two particles with masses \( m_1 = 2 \, \text{kg} \) and \( m_2 = 4 \, \text{kg} \), and their respective accelerations \( a_1 = 1 \, \text{m/s}^2 \) and \( a_2 = 2 \, \text{m/s}^2 \), we can follow these steps:

### Step 1: Identify the masses and their accelerations
- Mass of particle 1, \( m_1 = 2 \, \text{kg} \) with acceleration \( a_1 = 1 \, \text{m/s}^2 \)
- Mass of particle 2, \( m_2 = 4 \, \text{kg} \) with acceleration \( a_2 = 2 \, \text{m/s}^2 \)

### Step 2: Assign directions to the accelerations
- Let's assume the direction of the acceleration of the \( 2 \, \text{kg} \) mass (particle 1) is positive. Therefore, the acceleration of the \( 4 \, \text{kg} \) mass (particle 2) moving towards it will be considered negative.
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