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 distance between them
an increase in the volume of sphere 2
sphere 1
m = 50 kg
sphere 2
m = 20 kg

Explanation:

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

• The first option is wrong: All objects with mass have gravity, regardless of size.
• Second option: A decrease in \( r \) (distance) will increase \( F \) (since \( r \) is in the denominator, squaring it, so smaller \( r \) means larger \( F \)).
• Third option: An increase in \( r \) decreases \( F \) (opposite of what we want).
• Fourth option: Increasing the volume of sphere 2 doesn't directly mean its mass increases (density could change). Gravitational force depends on mass, not volume. So the correct factor is a decrease in distance.

Answer:

a decrease in the distance between them