Final answer:
The introduction of a liquid with a specific gravity around two masses doesn't change the gravitational force between them; therefore, the gravitational force remains the same (option c) F.
Step-by-step explanation:
The question concerns the gravitational force between two spheres of mass m in different mediums and how this force is affected when the space around the masses is filled with a liquid of a specific gravity. According to Newton's law of universal gravitation, the gravitational force is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
The formula for this force is F = G(M₁M₂)/R², where G is the gravitational constant, M₁ and M₂ are the masses of the two objects, and R is the distance between their centers.
Introducing a liquid with a specific gravity around the spheres does not alter the masses of the objects or the distance between them; therefore, the gravitational force remains unchanged. The specific gravity of the liquid only affects the buoyant force, which is related to Archimedes' principle and not to the gravitational force between two masses. Therefore, the correct option for the gravitational force when the space is filled with the liquid is (c) F.