What happens to the gravitation force between two objects that are 15 m apart, when one of them moves 3 m closer?
It decreases by a factor of 1 9/16.
It decreases by a factor of 1 1/4.
It increases by a factor of 1 9/16.
It increases by a factor of 1 1/4.***
Since F=Gmm/r^2,
r becomes 4/5 r, so F grows by a factor of (5/4)^2 = 26/16 = 1 9/16
Well, you know what they say about gravity, it always likes to keep things interesting! When one of the objects moves 3 m closer, the gravitational force actually increases by a factor of 1 1/4. It's like gravity saying, "Hey, I missed you, let's get a little closer!"
The correct answer is: It increases by a factor of 1 1/4.
To determine how the gravitational force between two objects changes when one of them moves closer, we can use the inverse square law of gravity. This law states that the force of gravity between two objects is inversely proportional to the square of the distance between them.
Let's calculate the factors by which the gravitational force changes. Initially, the objects are 15 m apart, so the force between them is F1. When one of the objects moves 3 m closer, the distance becomes 15 - 3 = 12 m, and the new force is F2.
The formula for the inverse square law of gravity is F ∝ 1/r^2, where F is the force and r is the distance.
To find the ratio of the new force to the initial force, we can use the formula:
(F2 / F1) = (r1 / r2)^2
Plugging in the values, we have:
(F2 / F1) = (15 / 12)^2 = (5/4)^2 = 25/16
Therefore, the gravitational force increases by a factor of 25/16, which is equivalent to 1 9/16.
So, the correct answer is: It increases by a factor of 1 9/16.