Multiple Choice
In Newton's law of universal gravitation, the magnitude of the gravitational force between two point masses is . Which two factors determine the value of for a given ?
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8. Centripetal Forces & Gravitation
Newton's Law of Gravity
Multiple Choice
In Newton's law of universal gravitation, , which two factors (besides the constant ) determine the magnitude of the gravitational force between two objects?
A
The distance between their centers and the objects' volumes
B
The masses of the two objects and the angle between their velocities
C
The electric charges of the objects and the distance between their centers
D
The masses of the two objects and the distance between their centers
Verified step by step guidance1
Recall Newton's law of universal gravitation, which states that the gravitational force \(F\) between two objects is given by the formula:
\[F = \frac{G m_1 m_2}{r^2}\]
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.
Identify the variables in the formula that affect the magnitude of the gravitational force. Notice that \(m_1\) and \(m_2\) appear in the numerator, meaning the force is directly proportional to the product of the two masses.
Observe that \(r\) appears in the denominator squared, indicating the force is inversely proportional to the square of the distance between the centers of the two objects.
Understand that other factors such as the objects' volumes, angles between velocities, or electric charges do not appear in this formula and therefore do not directly affect the gravitational force according to Newton's law.
Conclude that the two factors determining the magnitude of the gravitational force (besides the constant \(G\)) are the masses of the two objects and the distance between their centers.
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