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 \( v \) that must be given to the mass \( m \) at the centroid of an equilateral triangle formed by three uniform rods, we can follow these steps:

### Step 1: Understand the Configuration
We have three uniform rods of mass \( M \) and length \( l \) forming an equilateral triangle. The mass \( m \) is placed at the centroid of the triangle.

### Step 2: Calculate the Gravitational Potential Energy
The gravitational potential energy \( U \) of the mass \( m \) due to the rods needs to be calculated. Since the rods are not point masses, we will use integration to find the total potential energy.

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