Multiple Choice
Which statement best explains how Newton's law of universal gravitation shows that gravity is universal in nature?
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8. Centripetal Forces & Gravitation
Newton's Law of Gravity
Multiple Choice
In Newton's law of universal gravitation, , how does increasing the masses affect the gravitational force between two objects if the distance remains constant?
A
The gravitational force increases in direct proportion to the product .
B
The gravitational force increases in proportion to .
C
The gravitational force increases in direct proportion to the sum .
D
The gravitational force is independent of mass and depends only on .
Verified step by step guidance1
Recall Newton's law of universal gravitation, which states that the gravitational force \(F\) between two 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.
Note that in this formula, the force \(F\) is directly proportional to the product of the two masses \(m_1\) and \(m_2\). This means if either mass increases, the force increases proportionally.
Since the distance \(r\) remains constant, the denominator \(r^2\) does not change, so the only variables affecting the force are the masses.
Therefore, increasing the masses will increase the gravitational force in direct proportion to the product \(m_1 m_2\).
This means if you double one mass, the force doubles; if you double both masses, the force increases by a factor of four, illustrating the direct proportionality to the product of the masses.
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