What happens to the gravitational force between two objects if their separation is doubled? The force of attraction is doubled.
the same.
half as much.
one fourth as much.
force= constant/r^2 so if you double r, ...
The gravitational force between two objects follows an inverse square law. This means that if the separation between the objects is doubled, the force of attraction decreases by a factor of four (1/2^2). Therefore, the correct answer is one fourth as much.
To determine what happens to the gravitational force between two objects when their separation is doubled, we can use Newton's law of universal gravitation.
The 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, the equation for Newton's law of universal gravitation is:
F = G * (m1 * m2) / r^2
Where:
- F represents the gravitational force between the two objects
- G is the gravitational constant
- m1 and m2 are the masses of the two objects
- r is the separation between the centers of the two objects
If we double the separation between the objects by increasing 'r' by a factor of 2, we substitute this new value into the equation. The new separation is now '2r'.
So, the updated equation becomes:
F' = G * (m1 * m2) / (2r)^2
Now, let's compare the original force F with the new force F' by calculating their ratio:
F' / F = [G * (m1 * m2) / (2r)^2] / [G * (m1 * m2) / r^2]
Simplifying the equation, we get:
F' / F = [(m1 * m2) / (2r)^2] * [(r^2) / (m1 * m2)]
The mass terms and the square terms cancel out, leaving us with:
F' / F = 1 / 4
Therefore, the ratio of the new force F' to the original force F is 1/4 or one fourth as much. Thus, when the separation between two objects is doubled, the gravitational force between them becomes one fourth as much.