Question

two buckets of paint each have a mass of 9 kg. if the gravitational force between them is 6.0×10^(-10) n, how far apart are they?
a. 4.0 m
b. 1.8 m
c. 5.2 m
d. 3.0 m

Explanation:

Step1: Write the formula for gravitational force

The formula for gravitational force is \(F = G\frac{m_1m_2}{r^2}\), where \(F\) is the gravitational force, \(G = 6.67\times 10^{-11}\space Nm^2/kg^2\) (universal gravitational constant), \(m_1\) and \(m_2\) are the masses, and \(r\) is the distance between the centers of the two masses. Here \(m_1=m_2 = 9\space kg\) and \(F=6.0\times 10^{-10}\space N\).

Step2: Rearrange the formula to solve for \(r\)

From \(F = G\frac{m_1m_2}{r^2}\), we can get \(r^2=G\frac{m_1m_2}{F}\). Then \(r=\sqrt{G\frac{m_1m_2}{F}}\).
Substitute the values: \(G = 6.67\times 10^{-11}\space Nm^2/kg^2\), \(m_1 = m_2=9\space kg\), \(F = 6.0\times 10^{-10}\space N\)

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Answer:

D. \(3.0\space m\)