Question

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.

Rank these systems in order of decreasing gravitational force.

If rank items are equivalent, state as such; if the correct ranking cannot be determined, state as such.

Answer 1

Gravitational constant = G

System A

Mass of the first object = m

Mass of the second object = m

Distance between the two objects = r

Gravitational force between the two objects = F₁

System B

Mass of the first object = m

Mass of the second object = 2m

Distance between the two objects = 2r

Gravitational force between the two objects = F₂

System C

Mass of the first object = 2m

Mass of the second object = 3m

Distance between the two objects = 2r

Gravitational force between the two objects = F₃

System D

Mass of the first object = 4m

Mass of the second object = 5m

Distance between the two objects = 3r

Gravitational force between the two objects = F₄

Ranking the gravitational forces in decreasing order,

F₄ > F₃ > F₁ > F₂

Therefore ranking the systems,

D > C > A > B