Answer:
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:
[tex]F=G \frac{m_1 m_2}{r^2}[/tex]
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:
[tex]F=G\frac{m \cdot m}{r^2}=G \frac{m^2}{r^2}[/tex]
system B has masses m and 2m separated by a distance 2r:
[tex]F=G\frac{m \cdot 2m}{(2r)^2}=G \frac{2m^2}{4r^2}=\frac{1}{2} G \frac{m^2}{r^2}[/tex]
system C has masses 2m and 3m separated by a distance 2r:
[tex]F=G\frac{2m \cdot 3m}{(2r)^2}=G \frac{6m^2}{4r^2}=\frac{3}{2} G \frac{m^2}{r^2}[/tex]
system D has masses 4m and 5m separated by a distance 3r:
[tex]F=G\frac{4m \cdot 5m}{(3r)^2}=G \frac{20m^2}{9r^2}=\frac{20}{9} G \frac{m^2}{r^2}[/tex]
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
