System a has masses m and m separated by a distance r; system b has masses m and 2m separated by a distance 2r; system c has masses 2m and 3m separated by a distance 2r; and system d has masses 4m and 5m separated by a distance 3r. a) rank these systems in order of decreasing gravitational force.

System D --> System C --> System A --> System B

Explanation:

The gravitational force between two masses m1, m2 separated by a distance r is given by:

where G is the gravitational constant. Let's apply this formula to each case now to calculate the relative force for each system:

System A has masses m and m separated by a distance r:

system B has masses m and 2m separated by a distance 2r:

system C has masses 2m and 3m separated by a distance 2r:

system D has masses 4m and 5m separated by a distance 3r:

Now, by looking at the 4 different forces, we can rank them from the greatest to the smallest force, and we find:

System D --> System C --> System A --> System B