Binary stars of comparable masses `m_(1)` and `m_(2)` rotate under the influence of each other's gravity with a time period `T`. If they are stopped suddenly in their motions, find their relative velocity when they collide with each constant of gravitation.

Explanation

To solve the problem of finding the relative velocity of two binary stars of comparable masses \( m_1 \) and \( m_2 \) when they collide after being suddenly stopped, we can follow these steps:

### Step 1: Understanding the System
The binary stars are rotating around their common center of mass due to the gravitational attraction between them. When they are stopped suddenly, they will start to move towards each other due to gravity.

### Step 2: Finding the Center of Mass
The position of the center of mass (CM) of the two stars can be calculated using the formula:
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