What would be the result of the gravitational force between two objects, if the mass of an object doubles, and the other object's mass stays the same? (1 point) Responses The amount of the gravitational force decreases by one-half. The amount of the gravitational force decreases by one-half. The amount of the gravitational force remains the same The amount of the gravitational force remains the same The amount of the gravitational force quadruples The amount of the gravitational force quadruples The amount of the gravitational force doubles The amount of the gravitational force doubles
The correct response is:
The amount of the gravitational force doubles.
If the mass of one object doubles while the mass of the other object remains the same, the result would be that the amount of gravitational force between the two objects doubles.
To determine the result of the gravitational force between two objects when the mass of one object doubles while the other object's mass remains the same, you can use Newton's Law of Universal Gravitation, which states that the gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
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.