QuestionJuly 4, 2025

Two objects attract each other gravitationally. If the distance between their centers doubles, the gravitational force quadruples. doubles. is a half. is a fourth. Clear my selection

Two objects attract each other gravitationally. If the distance between their centers doubles, the gravitational force quadruples. doubles. is a half. is a fourth. Clear my selection
Two objects attract each other gravitationally. If the distance between their centers doubles, the gravitational force
quadruples.
doubles.
is a half.
is a fourth.
Clear my selection

Solution
3.2(292 votes)

Answer

is a fourth. Explanation 1. Identify the formula for gravitational force The gravitational force between two objects is given by **F = \frac{G \cdot m_1 \cdot m_2}{r^2}**, where G is the gravitational constant, m_1 and m_2 are the masses, and r is the distance between their centers. 2. Analyze the effect of doubling the distance If the distance r doubles, then the new distance becomes 2r. Substitute into the formula: **F' = \frac{G \cdot m_1 \cdot m_2}{(2r)^2} = \frac{G \cdot m_1 \cdot m_2}{4r^2}**. 3. Compare the new force to the original force The new force F' is \frac{1}{4} of the original force F.

Explanation

1. Identify the formula for gravitational force<br /> The gravitational force between two objects is given by **$F = \frac{G \cdot m_1 \cdot m_2}{r^2}$**, where $G$ is the gravitational constant, $m_1$ and $m_2$ are the masses, and $r$ is the distance between their centers.<br />2. Analyze the effect of doubling the distance<br /> If the distance $r$ doubles, then the new distance becomes $2r$. Substitute into the formula: **$F' = \frac{G \cdot m_1 \cdot m_2}{(2r)^2} = \frac{G \cdot m_1 \cdot m_2}{4r^2}$**.<br />3. Compare the new force to the original force<br /> The new force $F'$ is $\frac{1}{4}$ of the original force $F$.
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