Two objects, with masses m1 and m2, are originally a distance r apart, and the magnitude of the gravitational force on each one is f. the objects are moved a distance 2r apart. the new gravitational force: a) decreases 2 times
b) increases 2 times
c) decreases 4 times d) remains unchanged
e) increases 4 times

Explanation:

It is given that, two objects, with masses m₁ and m₂, are originally a distance r apart, and the magnitude of the gravitational force on each one is F. If the objects are moved a distance 2 r apart, we need to find the new gravitational force.

The gravitational force is given by :

...........(1)

Let the force is F' when the objects are moved a distance 2 r apart. So,

           (from equation (1))

So, it is clear that the magnitude of new force is F/4 i.e. decreases by a factor is 1/4. Hence, this is the required solution.