The distance between the two objects is 3.0 m
Explanation:
The magnitude of the gravitational force between two objects is given by the following equation:
[tex]F=G\frac{m_1 m_2}{r^2}[/tex]
where
:
[tex]G=6.67\cdot 10^{-11} m^3 kg^{-1}s^{-2}[/tex] is the gravitational constant
[tex]m_1,m_2[/tex] are the masses of the two objects
r is the separation between the objects
In this problem, we have:
[tex]m_1 = 2 kg[/tex] is the mass of the book
[tex]m_2 = 5 kg[/tex] is the mass of the vase
[tex]F=7.41\cdot 10^{-11}N[/tex] is the force between the two objects
Re-arranging the equation and solving for r, we find the distance between the two objects:
[tex]r=\sqr{\frac{Gm_1 m_2}{F}}=\sqrt{\frac{(6.67\cdot 10^{-11})(2)(5)}{7.41\cdot 10^{-11}}}=3.0 m[/tex]
Learn more about gravitational force:
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