In Newton’s law of universal gravitation, $F=G\frac{m{}_{1}m{}_2}{r^2}$, which two qualities of objects determine the strength of the gravitational force between them?

• A. Their masses and the distance between their centers
• B. Their electric charges and the distance between them
• C. Their masses and their speeds
• D. Their volumes and their densities

Answer: (A)

Verified step by step guidance

1. Recall Newton's law of universal gravitation, which states that the gravitational force \(F\) between two objects is given by the formula: \[F = G \frac{m_1 m_2}{r^2}\] 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.
2. Identify the variables in the formula that affect the gravitational force: the masses \(m_1\) and \(m_2\), and the distance \(r\) between the centers of the two objects.
3. Understand that the gravitational force increases with the product of the two masses, meaning larger masses result in a stronger force.
4. Recognize that the gravitational force decreases with the square of the distance between the objects, so increasing the distance reduces the force significantly.
5. Conclude that the two qualities determining the strength of the gravitational force are the masses of the objects and the distance between their centers.