Three mass points each of mass m are placed at the vertices of an equilateral triangle of side 1. What is the gravitational field and potential due to the three masses at the centroid of the triangle ?

Explanation

To solve the problem of finding the gravitational field and potential at the centroid of an equilateral triangle formed by three point masses, we can follow these steps:

### Step 1: Understand the Geometry
We have three point masses, each of mass \( m \), located at the vertices \( A \), \( B \), and \( C \) of an equilateral triangle with side length \( L = 1 \). The centroid \( D \) of the triangle is the point where we want to find the gravitational field and potential.

### Step 2: Calculate the Distance from the Centroid to a Vertex
The distance from the centroid \( D \) to any vertex (say \( A \)) can be calculated using the properties of the triangle. The centroid divides the median in a \( 2:1 \) ratio. The length of the median \( m \) of an equilateral triangle can be calculated using the formula:

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