How does increasing the distance between two masses affect gravitational force?

The correct answer to how increasing the distance between two masses affects the gravitational force is that the gravitational force decreases exponentially. This is based on Newton's law of universal gravitation, which states that the force of gravity ( F ) between two masses ( m_1 ) and ( m_2 ) is given by the formula:

[

F = G \frac{m_1 m_2}{r^2}

]

where ( G ) is the gravitational constant and ( r ) is the distance between the centers of the two masses. According to this formula, as the distance ( r ) increases, the gravitational force ( F ) decreases with the square of the distance. This means that if you were to double the distance, the force would become one-fourth of its original value. This relationship demonstrates an inverse square law, meaning the force decreases as the distance increases but not in a linear or exponential manner.

The other choices imply different relationships that do not accurately describe how gravitational force responds to distance changes. Saying the force increases inversely suggests that it would grow larger as distance increases, which contradicts the principle of gravitational attraction. Concluding that the gravitational force remains constant does not reflect the dependence on distance