Question

practice it!
two of the same sized soccer balls are 5 meters apart floating in space. they are then moved apart, placing
10 meters in between the two soccer balls.
which of the following has the greatest attraction?
both have the same attraction force
neither distance
10 meters apart
5 meters apart

Explanation:

To determine the gravitational attraction between two objects, we use Newton's law of universal gravitation: \( F = G\frac{m_1m_2}{r^2} \), where \( F \) is the gravitational force, \( G \) is the gravitational constant, \( m_1 \) and \( m_2 \) are the masses of the two objects, and \( r \) is the distance between their centers.

In this problem, the two soccer balls have the same mass (since they are the same sized and presumably same material, so same mass) and \( G \) is a constant. So the force \( F \) is inversely proportional to the square of the distance \( r \) between them (\( F \propto \frac{1}{r^2} \)).

This means that as the distance \( r \) decreases, the gravitational force \( F \) increases, and as \( r \) increases, \( F \) decreases.

The two distances given are 5 meters and 10 meters. Since 5 meters is less than 10 meters, the gravitational attraction (force) between the two soccer balls will be greater when they are 5 meters apart (because a smaller distance leads to a larger force, according to the inverse - square relationship in Newton's law of gravitation).

Answer:

5 meters apart