Final answer:
The force of gravitation between two balls with equal mass and density is proportional to the square of their radius, consistent with Newton's law of gravitation.
Step-by-step explanation:
The force of gravitation between two balls, each of radius r, having equal mass and density, is determined by Newton's universal law of gravitation. According to this law, the gravitational force (F) is directly proportional to the product of their masses (m1 and m2) and inversely proportional to the square of the distance (r) between their centers. Since the masses of the balls are proportional to their volumes and the volume of a sphere is proportional to the cube of its radius (r³), the mass of each ball is proportional to r³.
Therefore, the gravitational force equation for the two balls in contact is:
F ∼ m1 × m2 / r² ∼ (r³ × r³) / r² ∼ r&sup4; / r² ∼ r².
Thus, the force of gravitation between the two spheres when placed in contact is proportional to the square of the radius r, which corresponds to option (b). The correct option is not directly r, r³, or inversely proportional to r, but it is proportional to r².