The correct response is:
The amount of the gravitational force doubles.
The amount of the gravitational force doubles.
Mathematically, this can be expressed as:
F = (G * m1 * m2) / r^2
Where:
F is the gravitational force between the objects,
G is the gravitational constant,
m1 and m2 are the masses of the objects, and
r is the distance between their centers.
Since we are considering a scenario where the mass of one object doubles while the other object's mass remains the same, let's assume m1 is the initial mass and m1' is the new mass of the first object.
The gravitational force for the initial scenario can be represented as:
F_initial = (G * m1 * m2) / r^2
For the new scenario where the mass of the first object doubles, the gravitational force would be:
F_new = (G * 2m1 * m2) / r^2
To compare the two scenarios, we can simplify F_new:
F_new = (2 * G * m1 * m2) / r^2
= 2 * (G * m1 * m2) / r^2
= 2 * F_initial
Therefore, the result is that the gravitational force doubles when the mass of one object doubles while the other object's mass remains the same. Finally, the correct answer is: The amount of the gravitational force doubles.