Question
What happens to the gravitational force between two objects if the distance between them triples?
(1 point)
The force increases by a factor of 9.
The force decreases by a factor of 9.
The force increases by a factor of 3.
The force decreases by a factor of 3.
(1 point)
The force increases by a factor of 9.
The force decreases by a factor of 9.
The force increases by a factor of 3.
The force decreases by a factor of 3.
Answers
GPT-4o mini
The gravitational force between two objects is described by Newton's law of universal gravitation, which states that the force \( F \) is inversely proportional to the square of the distance \( r \) between their centers:
\[
F \propto \frac{1}{r^2}
\]
If the distance between the two objects triples (i.e., becomes \( 3r \)), the new gravitational force \( F' \) can be expressed as:
\[
F' \propto \frac{1}{(3r)^2} = \frac{1}{9r^2}
\]
This shows that the new force \( F' \) is \( \frac{1}{9} \) of the original force \( F \):
\[
F' = \frac{F}{9}
\]
Therefore, if the distance between the two objects triples, the gravitational force decreases by a factor of 9.
The correct answer is: **The force decreases by a factor of 9.**
\[
F \propto \frac{1}{r^2}
\]
If the distance between the two objects triples (i.e., becomes \( 3r \)), the new gravitational force \( F' \) can be expressed as:
\[
F' \propto \frac{1}{(3r)^2} = \frac{1}{9r^2}
\]
This shows that the new force \( F' \) is \( \frac{1}{9} \) of the original force \( F \):
\[
F' = \frac{F}{9}
\]
Therefore, if the distance between the two objects triples, the gravitational force decreases by a factor of 9.
The correct answer is: **The force decreases by a factor of 9.**