9) The gravitational force increases by a factor of 16
10) The gravitational force decreases by a factor of 4
Explanation:
9)
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
[tex]m_1, m_2[/tex] are the masses of the two objects
r is the separation between them
Let's call F the initial force between the two objects. Later, the distance is reduced to 1/4 of the initial distance, so that
[tex]d'=\frac{1}{4}d[/tex]
Substituting into the equation, we find the new gravitational force between the objects:
[tex]F'=G\frac{m_1 m_2}{r'^2}=G\frac{m_1 m_2}{(r/4)^2}=16(G\frac{m_1 m_2}{r^2}=16F[/tex]
So, the force increases by a factor of 16.
10)
Again, let's call the original force between the objects
[tex]F=G\frac{m_1 m_2}{r^2}[/tex]
In this problem, the distance between the objects is doubled, so this time we have
[tex]d'=2d[/tex]
Now we can substitute into the previous equation, so we find the new gravitational force between the objects:
[tex]F'=G\frac{m_1 m_2}{r'^2}=G\frac{m_1 m_2}{(2r)^2}=\frac{1}{4}(G\frac{m_1 m_2}{r^2}=\frac{F}{4}[/tex]
So, the force decreases by a factor of 4.
Learn more about gravitational force:
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