Multiple Choice
According to Newton's law of universal gravitation, the magnitude of the gravitational force between two point masses depends on which two factors?
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8. Centripetal Forces & Gravitation
Newton's Law of Gravity
Multiple Choice
In Newton's law of universal gravitation, the magnitude of the gravitational force between two point masses is . Which factors affect the strength of the gravitational force?
A
It depends only on the distance between the objects, not on their masses.
B
It depends on the masses and increases proportionally with .
C
It depends on the electric charges of the objects and the distance between them.
D
It depends on the two masses and and inversely on the square of the distance between them.
Verified step by step guidance1
Recall Newton's law of universal gravitation, which states that the gravitational force \(F\) between two point masses \(m_1\) and \(m_2\) separated by a distance \(r\) is given by the formula:
\[F = G \frac{m_1 m_2}{r^2}\]
where \(G\) is the gravitational constant.
Identify the variables in the formula: the force \(F\) depends directly on the product of the two masses \(m_1\) and \(m_2\), meaning if either mass increases, the force increases proportionally.
Notice that the force depends inversely on the square of the distance \(r\) between the two masses. This means that as the distance increases, the force decreases by the factor of \(r^2\).
Understand that the gravitational force does not depend on electric charges or any other properties besides the masses and the distance between them.
Summarize that the strength of the gravitational force is affected by both masses and the distance between them, increasing with larger masses and decreasing with greater distance squared.
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