Question

what would cause an increase in the force of gravity between the two spheres shown?
the spheres are too small to have any force of gravity between them
a decrease in the distance between them
an increase in the volume of sphere 2
an increase in the distance between them

Explanation:

Step1: Recall gravity formula

The gravitational force formula between two objects is $F = G\frac{m_1m_2}{r^2}$, where $G$ is the gravitational - constant, $m_1$ and $m_2$ are the masses of the two objects, and $r$ is the distance between their centers of mass.

Step2: Analyze each option

• Option 1: All objects with mass have a gravitational force between them, so this is incorrect.
• Option 2: Decreasing the distance $r$ between the two spheres in the formula $F = G\frac{m_1m_2}{r^2}$ will increase the value of $F$ since $F$ is inversely proportional to $r^2$.
• Option 3: Increasing the volume of a sphere does not directly increase the gravitational force. Mass, not volume, is in the gravitational - force formula.
• Option 4: Increasing the distance $r$ between the two spheres will decrease the gravitational force $F$ according to the formula $F = G\frac{m_1m_2}{r^2}$.

Answer:

a decrease in the distance between them