Question

which of the following has the greatest attraction?
5 meters apart
neither distance
10 meters apart
both have the same attraction force

Explanation:

Step1: Recall gravitational - force formula

The gravitational force between two objects is given by $F = G\frac{m_1m_2}{r^{2}}$, where $G$ is the gravitational constant, $m_1$ and $m_2$ are the masses of the two objects, and $r$ is the distance between them. Assuming the masses of the objects remain the same, the force is inversely proportional to the square of the distance $r$.

Step2: Compare the distances

When $r_1 = 5$m and $r_2=10$m, since $F\propto\frac{1}{r^{2}}$, a smaller distance $r$ will result in a larger force $F$. So the attraction is greater when the objects are 5 meters apart.

Answer:

5 meters apart