Question

The gravitational force between two objects is 2000 N. The mass of each object is reduced to one-third of its original mass.

How must the distance between the objects change to keep the gravitational force between them 2000 N?

The distance must be one-ninth the original distance.
The distance must be one-third the original distance.
The distance must be three times greater.
The distance must be nine times greater.

Answer 1

Answer: The distance must be one-third the original distance.

Reason: F ∝ m1 m2 / r^2. Reducing each mass to 1/3 multiplies m1 m2 by (1/3)*(1/3)=1/9, so to keep F the same r^2 must also be multiplied by 1/9, hence r must be multiplied by 1/3.