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 amount of gravitational force remains the same. According to Newton's Law of Universal Gravitation, the force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. Therefore, doubling the mass of one object while keeping the distance constant has no effect on the gravitational force between them.
To determine what happens to the gravitational force between two objects when the mass of one doubles, we can use Newton's law of universal gravitation. This law 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.
Mathematically, this can be expressed as:
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, and r is the distance between them.
In this scenario, we assume that the distance between the two objects remains the same. Therefore, we can focus on how the mass of one of the objects affects the gravitational force.
If the mass of an object doubles while the other parameters remain constant, we can substitute the new values into the equation:
F' = G * (2m * m) / r^2
Simplifying this equation, we get:
F' = 2 * (G * (m * m) / r^2)
Comparing this to the original equation, we see that the new gravitational force F' is twice the original force F. Therefore, the amount of gravitational force between the two objects doubles when the mass of one object doubles, assuming the distance remains the same.
Therefore, the correct answer is: "the amount of the gravitational force doubles."