1) The new gravitational force is half of the original force
2) The new gravitational force is 1/8 of the original force
Explanation:
1)
Let's call F the initial gravitational force between the object A and B. The magnitude of F is given by the equation
The magnitude of the gravitational force between two objects is given by
[tex]F=G\frac{m_A m_B}{R^2}[/tex]
where
[tex]G=6.67\cdot 10^{-11} m^3 kg^{-1}s^{-2}[/tex] is the gravitational constant
[tex]m_A,m_B[/tex] are the masses of the two objects
R is the separation between them
In this part of the problem, we are told that the distance between the two objects doubles, so the new distance is
R' = 2R
While the mass of object A is doubled, so the new mass is
[tex]m_A' = 2m_A[/tex]
Therefore, the new gravitational force is
[tex]F' = \frac{Gm_A' m_B}{R'^2}= \frac{G(2m_A) m_B}{(2R)^2}=\frac{1}{2}(\frac{Gm_A m_B}{R^2})=\frac{F}{2}[/tex]
Therefore, the new force is half of the original force.
2)
In this second part of the problem, the distance between the two objects doubles, so the new distance is
R' = 2R
While the mass of object A is halved, so the new mass is
[tex]m_A' = \frac{m_A}{2}[/tex]
Therefore, the new gravitational force this time is:
[tex]F' = \frac{Gm_A' m_B}{R'^2}= \frac{G(m_A/2) m_B}{(2R)^2}=\frac{1}{8}(\frac{Gm_A m_B}{R^2})=\frac{F}{8}[/tex]
Therefore, the new force is 1/8 of the original force.
Learn more about gravitational force:
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