Three mass points each of mass m are placed at the vertices of an equilateral tringale of side l. What is the gravitational field and potential due to three masses at the centroid of the triangle ?

Explanation

To find the gravitational field and potential at the centroid of an equilateral triangle formed by three mass points, we can follow these steps:

### Step 1: Understand the Geometry
We have three mass points, each of mass \( m \), located at the vertices \( A \), \( B \), and \( C \) of an equilateral triangle with side length \( l \). The centroid \( O \) of the triangle is the point where the three medians intersect.

### Step 2: Calculate the Distance from the Centroid to a Vertex
The distance \( R \) from the centroid \( O \) to any vertex (say \( A \)) of the triangle can be calculated using the formula:
\[
...