Two balls of mass `m` each are placed at the two vertices of an equilateral triangle. Another ball of mass `2m` is placed at the third vertex of the triangle. Locate the centre of mass of the system.

Explanation

To locate the center of mass of the system consisting of two balls of mass `m` at two vertices of an equilateral triangle and another ball of mass `2m` at the third vertex, we can follow these steps:

### Step 1: Define the Coordinates
Let's assume the vertices of the equilateral triangle are as follows:
- Vertex A (where the ball of mass `2m` is located) at coordinates (0, 0)
- Vertex B (where one ball of mass `m` is located) at coordinates (l, 0)
- Vertex C (where the other ball of mass `m` is located) at coordinates (l/2, (√3/2)l)

...