Question

which change will always result in an increase in the gravitational force between two objects?
increasing the masses of the objects and increasing the distance between the objects
decreasing the masses of the objects and decreasing the distance between the objects
increasing the masses of the objects and decreasing the distance between the objects
decreasing the masses of the objects and increasing the distance between the objects

Explanation:

Step1: Recall gravitational force law

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

Step2: Analyze mass effect on force

Force is directly proportional to the product of masses ($F \propto m_1m_2$). Increasing masses increases $F$.

Step3: Analyze distance effect on force

Force is inversely proportional to the square of distance ($F \propto \frac{1}{r^2}$). Decreasing distance increases $F$.

Step4: Evaluate each option

• Option1: Increasing masses (+F) but increasing distance (-F) → Net change not guaranteed increase.
• Option2: Decreasing masses (-F) and decreasing distance (+F) → Net change not guaranteed increase.
• Option3: Increasing masses (+F) and decreasing distance (+F) → Both changes increase $F$, so total force always increases.
• Option4: Decreasing masses (-F) and increasing distance (-F) → Net force decreases.

Answer:

increasing the masses of the objects and decreasing the distance between the objects