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?
O The amount of the gravitational force decreases by one-half.
O The amount of the gravitational force quadruples.
O The amount of the gravitational force doubles.
O The amount of the gravitational force remains the same.
The amount of the gravitational force doubles.
The amount of 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.
In this case, the mass of one object doubles while the mass of the other remains the same. Since the doubling of the mass will be reflected in the product of their masses, the gravitational force between them will also double.
Therefore, the correct answer is: The amount of the gravitational force doubles.
According to Newton's law of universal gravitation, 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.
To determine what happens to the gravitational force when the mass of one object doubles and the distance remains the same, we need to consider the formula for gravitational force:
F = (G * m1 * m2) / r^2
Where:
F = gravitational force
G = gravitational constant
m1, m2 = masses of the two objects
r = distance between the centers of the two objects
Let's assume the mass of one object doubles, while the mass of the other object remains the same. We can represent the new masses as m' for the doubled mass and m for the unchanged mass. The distance between them remains the same, so we can represent it as r in both cases.
Using this information, we can compare the initial gravitational force (F1) to the new gravitational force (F2):
F1 = (G * m * m) / r^2
F2 = (G * (2m) * m) / r^2
Simplifying both equations, we get:
F1 = (G * m^2) / r^2
F2 = (2G * m^2) / r^2
Comparing F1 and F2, we see that F2 is equal to twice F1:
F2 = 2 * F1
This means that when the mass of one object doubles, while the mass of the other object remains the same, the gravitational force between them also doubles.
So, the correct answer is:
O The amount of the gravitational force doubles.