Three particles of masses 1.0 kg 2.0 kg and 3.0 kg are placed at the corners A,B and C respectively of an equilateral triangle ABC of edge 1m. Locate the centre of mass of the system.

Explanation

To find the center of mass of the system of three particles located at the corners of an equilateral triangle, we can follow these steps:

### Step 1: Define the coordinates of the particles
Let's assign coordinates to the corners of the equilateral triangle ABC:
- Mass \( m_1 = 1.0 \, \text{kg} \) at point A (0, 0)
- Mass \( m_2 = 2.0 \, \text{kg} \) at point B (0.5, \( \frac{\sqrt{3}}{2} \)) since the height of the triangle is \( \frac{\sqrt{3}}{2} \) when the base is 1 meter.
- Mass \( m_3 = 3.0 \, \text{kg} \) at point C (1, 0)

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