How does the gravitational force between earth and the moon change when the distance between the two objects doubles but mass doesnt change?
A. The gravitational force between earth, and the moon will completely disappear.B. The gravitational force between earth, and the moon would go up by proportional amount.C. The gravitational force between earth, and the moon will go down by proportional amount.D. The gravitational force between earth and the moon would stay the same.
C. The gravitational force between earth and the moon will go down by proportional amount.
C. The gravitational force between earth and the moon will go down by a proportional amount.
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 their centers.
If the distance between the Earth and the Moon doubles, the new distance would be twice the original distance. Since the gravitational force is inversely proportional to the square of the distance, it would decrease by a factor of four (2^2) when the distance doubles. Therefore, the gravitational force between Earth and the Moon will go down by a proportional amount, option C.
To determine how the gravitational force between Earth and the Moon changes when the distance between them doubles but their masses remain the same, we can use Newton's law of universal gravitation.
According to Newton's law, the gravitational force between two objects is inversely proportional to the square of the distance between them. Mathematically, the equation is:
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 the objects.
Now, let's consider the scenario where the distance between Earth and the Moon doubles. If we represent the original distance as r, then the new distance would be 2r. Plugging this into the equation, we get:
F' = G * (m1 * m2) / (2r)^2
Simplifying this equation further, we have:
F' = G * (m1 * m2) / 4r^2
As we can see, the new gravitational force (F') is equal to one-fourth of the original gravitational force (F).
Therefore, the correct answer to the question is C. The gravitational force between Earth and the Moon will go down by a proportional amount when the distance between the two objects doubles but the mass doesn't change.