QuestionJune 10, 2025

6. Two spherical objects have masses of 6.3times 103kg and 3.5times 104kg .The gravitational attraction between them is 6.5times 10-3N How far apart are their centers?

6. Two spherical objects have masses of 6.3times 103kg and 3.5times 104kg .The gravitational attraction between them is 6.5times 10-3N How far apart are their centers?
6. Two spherical objects have masses of 6.3times 103kg and 3.5times 104kg .The
gravitational attraction between them is 6.5times 10-3N How far apart are their
centers?

Solution
4.2(296 votes)

Answer

1.502 meters Explanation 1. Identify the formula for gravitational force The gravitational force between two masses is given by **F = \frac{G \cdot m_1 \cdot m_2}{r^2}**, where F is the force, G is the gravitational constant (6.674 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2), m_1 and m_2 are the masses, and r is the distance between their centers. 2. Rearrange the formula to solve for distance Rearrange to find r: **r = \sqrt{\frac{G \cdot m_1 \cdot m_2}{F}}**. 3. Substitute values into the formula Substitute G = 6.674 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2, m_1 = 6.3 \times 10^3 \, \text{kg}, m_2 = 3.5 \times 10^4 \, \text{kg}, and F = 6.5 \times 10^{-3} \, \text{N} into the formula: r = \sqrt{\frac{(6.674 \times 10^{-11}) \cdot (6.3 \times 10^3) \cdot (3.5 \times 10^4)}{6.5 \times 10^{-3}}}. 4. Calculate the distance Compute the value: r = \sqrt{\frac{1.4667 \times 10^{-2}}{6.5 \times 10^{-3}}} = \sqrt{2.25646} \approx 1.502 meters.

Explanation

1. Identify the formula for gravitational force<br /> The gravitational force between two masses is given by **$F = \frac{G \cdot m_1 \cdot m_2}{r^2}$**, where $F$ is the force, $G$ is the gravitational constant ($6.674 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2$), $m_1$ and $m_2$ are the masses, and $r$ is the distance between their centers.<br /><br />2. Rearrange the formula to solve for distance<br /> Rearrange to find $r$: **$r = \sqrt{\frac{G \cdot m_1 \cdot m_2}{F}}$**.<br /><br />3. Substitute values into the formula<br /> Substitute $G = 6.674 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2$, $m_1 = 6.3 \times 10^3 \, \text{kg}$, $m_2 = 3.5 \times 10^4 \, \text{kg}$, and $F = 6.5 \times 10^{-3} \, \text{N}$ into the formula: <br /> $r = \sqrt{\frac{(6.674 \times 10^{-11}) \cdot (6.3 \times 10^3) \cdot (3.5 \times 10^4)}{6.5 \times 10^{-3}}}$.<br /><br />4. Calculate the distance<br /> Compute the value: $r = \sqrt{\frac{1.4667 \times 10^{-2}}{6.5 \times 10^{-3}}} = \sqrt{2.25646} \approx 1.502$ meters.
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