Two stars of masses M and 4M have radii x and 3x respectively. The distance between centres of two stars is 12x. A body of mass m is fired from the surface of bigger sphere towards smaller sphere. Find the minimum initial speed (in terms of G, x, M) required to reach the surface of smaller star.

Explanation

To find the minimum initial speed required for a body of mass \( m \) to reach the surface of the smaller star, we will use the conservation of energy principle. We will analyze the gravitational potential energy and kinetic energy at two different points: the surface of the larger star and the surface of the smaller star.

### Step-by-Step Solution:

1. **Identify the masses and distances:**
- Mass of the larger star, \( M_1 = 4M \)
- Radius of the larger star, \( R_1 = 3x \)
- Mass of the smaller star, \( M_2 = M \)
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