In Newton's law of universal gravitation, the magnitude of the gravitational force between two point masses is $F=G\frac{m{1}_{\mathrm{}}m{2}_{\mathrm{}}}{r^2}$. Which two factors determine the strength of the gravitational force?

• A. The masses of the two objects and the volume of the larger object
• B. The distance between the objects and the acceleration due to gravity $g$ at Earth's surface
• C. The electric charges of the objects and the distance between them
• D. The masses of the two objects and the distance between their centers

Answer: (D)

Verified step by step guidance

1. Recall Newton's law of universal gravitation, which states that the gravitational force \(F\) between two point 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.
2. Identify the variables in the formula that affect the magnitude of the gravitational force: the masses \(m_1\) and \(m_2\), and the distance \(r\) between them.
3. Understand that the gravitational force increases with larger masses because the force is directly proportional to the product \(m_1 m_2\).
4. Recognize that the gravitational force decreases as the distance \(r\) between the two masses increases, since the force is inversely proportional to the square of the distance \(r^2\).
5. Conclude that the two factors determining the strength of the gravitational force are the masses of the two objects and the distance between their centers.