The mass of an object doubles. What happens to the gravitational force between it and another object whose mass stays the same, assuming they remain the same distance apart?(1 point)
Responses
The amount of the gravitational force quadruples.
The amount of the gravitational force quadruples.
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 doubles.
The amount of the gravitational force doubles.
The amount of the gravitational force remains the same.
The amount of the gravitational force doubles.
The amount of the gravitational force doubles.
To find the answer to this question, we can use Newton's law of 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 them.
Let's denote the mass of the first object as m1, the mass of the second object as m2, and the initial gravitational force between them as F. Since the mass of the first object doubles while the mass of the second object remains the same, we can write the new masses as 2m1 and m2.
Using Newton's law of gravitation, the gravitational force between the two objects can be expressed as F = G * (m1 * m2) / r^2, where G is the gravitational constant and r is the distance between the two objects.
Now, let's consider what happens when the mass of the first object doubles. The new mass of the first object is 2m1. Plugging these values into the equation, we get:
New gravitational force, F_new = G * (2m1 * m2) / r^2.
Simplifying this equation, we have:
F_new = (2 * G * m1 * m2) / r^2.
Comparing this to the original gravitational force F, we can see that the new gravitational force is twice the original force:
F_new = 2F.
Therefore, the correct answer is: The amount of the gravitational force doubles.