Final answer:
The false statement is option c. The gravitational force between two planets depends on both of their masses, which is governed by Newton's Universal Law of Gravitation.
Step-by-step explanation:
The correct answer to the student's question is option c. The gravitational force between two masses is dependent on both of their masses. According to Newton's Universal Law of Gravitation, the gravitational force (F) between two objects 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:
F = G * (m1 * m2) / r^2
Where G is the gravitational constant.
Now, addressing the multiple-choice options:
- Planet Y having a greater gravitational force than Planet X (option a) is true because it has a larger mass.
- Planet Y having a smaller gravitational acceleration than Planet X (option b) can be true if we assume both planets have the same radius, since acceleration due to gravity (g) on the surface of a planet is g = G * m / r^2, and the larger mass of Planet Y will lead to greater g if radii are the same.
- The gravitational force being independent of their masses (option c) is false, as explained above.
- Planet X has a greater gravitational acceleration than Planet Y (option d) contradicts option b and would depend on their radii.