Multiple Choice
In Newton's law of universal gravitation, , which factors determine the magnitude of the gravitational force between two objects?
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8. Centripetal Forces & Gravitation
Newton's Law of Gravity
Multiple Choice
According to Newton's law of universal gravitation, , which change will increase the gravitational force between two objects?
A
Increase the distance between the objects while keeping and constant
B
Decrease both masses and while keeping constant
C
Decrease the distance between the objects while keeping and constant
D
Keep , , and the same but move the objects to a higher altitude above Earth
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:
\[F = \frac{G m_1 m_2}{r^2}\]
where \(G\) is the gravitational constant.
Analyze how each variable affects the force:
- The force \(F\) is directly proportional to the product of the masses \(m_1\) and \(m_2\). This means if either mass increases, the force increases.
- The force \(F\) is inversely proportional to the square of the distance \(r\). This means if the distance increases, the force decreases, and if the distance decreases, the force increases.
Evaluate the effect of increasing the distance \(r\) while keeping the masses constant:
Since \(F\) is inversely proportional to \(r^2\), increasing \(r\) will decrease the force.
Evaluate the effect of decreasing both masses \(m_1\) and \(m_2\) while keeping \(r\) constant:
Since \(F\) is directly proportional to the product \(m_1 m_2\), decreasing both masses will decrease the force.
Evaluate the effect of decreasing the distance \(r\) while keeping the masses constant:
Since \(F\) is inversely proportional to \(r^2\), decreasing \(r\) will increase the force, making this the correct way to increase the gravitational force between the two objects.
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