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
where
is the gravitational constant
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
Therefore, the new gravitational force is
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
Therefore, the new gravitational force this time is:
Therefore, the new force is 1/8 of the original force.
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