The mass of an object doubles. What happens to the gravitational force between it and another object, assuming they remain the same distance apart?
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 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. If the mass of one object doubles, the gravitational force between the two objects also doubles.
To determine what happens to the gravitational force between two objects when the mass of one object doubles, we can use the formula for gravitational force:
F = G * (m1 * m2) / r^2
Where:
F represents the gravitational force between the two objects,
G is the gravitational constant,
m1 and m2 represent the masses of the two objects, and
r represents the distance between the centers of the two objects.
Assuming the distance between the objects remains the same, we can focus on the relationship between the masses (m1 and m2).
When the mass of an object doubles, let's say the mass of object 1 doubles, m1 becomes 2 * m1 (original mass of object 1). The mass of object 2 remains the same, so m2 remains m2.
Plugging these new values into the gravitational force equation, we get:
F = G * (2 * m1 * m2) / r^2
Now let's compare this to the original gravitational force equation:
F = G * (m1 * m2) / r^2
To find the change in gravitational force, we can take the ratio of the new gravitational force to the original gravitational force:
New force / Original force = (G * (2 * m1 * m2) / r^2) / (G * (m1 * m2) / r^2)
Simplifying this expression, we find that the G, r^2, and m2 terms cancel out:
New force / Original force = (2 * m1 * m2) / (m1 * m2)
The m2 terms also cancel out:
New force / Original force = 2
Therefore, the new gravitational force is twice the original gravitational force.
Hence, the answer is: The amount of the gravitational force doubles.