Three identical point objects each of mass `m` are placed at the vertices of an equilateral triange of side `l`. What is the gravitational potential at the centre of the equilateral triangle due to the point masses?

Explanation

To find the gravitational potential at the center of an equilateral triangle due to three identical point masses located at its vertices, we can follow these steps:

### Step 1: Understand the Configuration
We have three identical point masses, each of mass \( m \), placed at the vertices of an equilateral triangle with side length \( l \). The center of the triangle is also known as the centroid.

### Step 2: Determine the Distance from the Centroid to the Vertices
The distance from the centroid (center) to any vertex of the equilateral triangle can be calculated using the formula for the centroid of a triangle. The centroid divides the median in the ratio \( 2:1 \). The length of the median \( m \) of an equilateral triangle is given by:

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