The mass of each ball is [tex]4.76\cdot 10^6 kg[/tex]
Explanation:
The magnitude of the gravitational force between two objects is given by
[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
m1, m2 are the masses of the two objects
r is the separation between them
In this problem, we have:
r = 12.0 m is the distance between the two balls
[tex]m_1 = m_2 = m[/tex] is the mass of each ball (they have same mass, so we call it [tex]m[/tex])
[tex]F=10.5 N[/tex] is the gravitational force between the two ball
Solving for m, we find the mass of each ball:
[tex]F=\frac{Gm^2}{r^2}\\m=\sqrt{\frac{Fr^2}{G}}=\sqrt{\frac{(10.5)(12.0)^2}{6.67\cdot 10^{-11}}}=4.76\cdot 10^6 kg[/tex]
Learn more about gravitational force:
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