Three point masses `m_(1) = 2Kg, m_(2) = 4kg and m_(3)= 6kg` are kept at the three corners of an equilateral triangle of side 1 m. Find the locationo of their center of mass.

Explanation

To find the center of mass of the three point masses located at the corners of an equilateral triangle, we will follow these steps:

### Step 1: Define the positions of the masses
Let’s place the equilateral triangle in the coordinate system:
- Mass \( m_1 = 2 \, \text{kg} \) at point \( A(0, 0) \)
- Mass \( m_2 = 4 \, \text{kg} \) at point \( B(1, 0) \)
- Mass \( m_3 = 6 \, \text{kg} \) at point \( C\left(\frac{1}{2}, \frac{\sqrt{3}}{2}\right) \)

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