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Two stars of masses M and 4M have radii ...

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.

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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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