Three point masses m1, m2, m3 are placed at the corners of an equilateral triangle of side 2 m. Locate the centre of mass of the system.
`m_(1)=2kg, m_(2)=3kg, m_(3)=4kg`

Explanation

To locate the center of mass of the system of three point masses \( m_1, m_2, m_3 \) placed at the corners of an equilateral triangle, we will follow these steps:

### Step 1: Define the coordinates of the triangle's vertices
We have three masses located at the corners of an equilateral triangle with a side length of 2 m. We can place the triangle in the coordinate system as follows:
- Mass \( m_1 = 2 \, \text{kg} \) at \( A(0, 0) \)
- Mass \( m_2 = 3 \, \text{kg} \) at \( B(2, 0) \)
- Mass \( m_3 = 4 \, \text{kg} \) at \( C(1, \sqrt{3}) \) (using the height of the triangle, which is \( \sqrt{3} \) when the side is 2 m)

...