Find the centre of mass of three particle at the vertices of an equilateral triangle. The masses of the particle are `100g, 150 g, and 200g` respectively. Each side of the equilateral triangle is `0.5m` along.

Explanation

To find the center of mass of three particles located at the vertices of an equilateral triangle, we will follow these steps:

### Step 1: Define the coordinates of the particles
Let's place the equilateral triangle in the xy-plane. We can assign the following coordinates to the particles based on their masses and positions:

- Particle 1 (mass \( m_1 = 100 \, \text{g} \)) at vertex A: \( (0, 0) \)
- Particle 2 (mass \( m_2 = 150 \, \text{g} \)) at vertex B: \( (0.5, 0) \)
- Particle 3 (mass \( m_3 = 200 \, \text{g} \)) at vertex C: To find the coordinates of C, we need to calculate the height of the triangle. The height \( h \) of an equilateral triangle can be calculated using the formula:
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