11. 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
The amount of the gravitational force decreases by one-half.
The amount of the gravitational force quadruples.
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 determine what happens to the gravitational force between two objects when the mass of one object doubles while the other object's mass remains the same, we can use Newton's law of universal gravitation:
F = (G * m1 * m2) / r^2
Where:
F is the gravitational force
G is the gravitational constant
m1 and m2 are the masses of the two objects
r is the distance between the two objects
Considering that the distance remains the same, and only the mass of one object changes, we can compare the initial gravitational force (F1) to the final gravitational force (F2). Let's assume the initial mass of the object is m1 and the mass of the other object is m2.
F1 = (G * m1 * m2) / r^2
F2 = (G * (2m1) * m2) / r^2
To find the relationship between F1 and F2, we divide F2 by F1:
(F2 / F1) = [(G * (2m1) * m2) / r^2] / [(G * m1 * m2) / r^2]
(F2 / F1) = [(2m1 * m2) / m1 * ((G * m1 * m2) / r^2)]
(F2 / F1) = (2m1 * m2) / (m1 * m2)
Simplifying the equation:
(F2 / F1) = 2
From the equation, we can conclude that the final gravitational force (F2) is twice the initial gravitational force (F1) when the mass of one object doubles while the mass of the other object remains the same. Therefore, the correct answer is:
The amount of the gravitational force doubles.