Three uniform rods, each of mass `M` and length `l`, are connected to form an equilateral triangle in a gravity free space. Another small body of mass `m` is kept at the centroid. Find the minimum velocity `v` to be given to mass `m` so that it escapes the gravitational pull of the triangle.

Explanation

To solve the problem of finding the minimum velocity \( v \) required for the mass \( m \) at the centroid of the equilateral triangle formed by three uniform rods to escape their gravitational pull, we will follow these steps:

### Step 1: Understand the System
We have three uniform rods, each of mass \( M \) and length \( l \), arranged in the form of an equilateral triangle. A small mass \( m \) is placed at the centroid of this triangle. The goal is to determine the minimum velocity \( v \) that needs to be imparted to mass \( m \) so that it can escape the gravitational influence of the rods.

### Step 2: Calculate the Gravitational Potential Energy
The gravitational potential energy \( U \) of the mass \( m \) due to the rods needs to be calculated. The potential energy due to a small element of mass \( dm \) from one of the rods at a distance \( r \) from mass \( m \) is given by:

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