Question

Object A and Object B are equal distances on opposite sides of Object C. Object B has three times the mass of Object C. Objects A and B have equal mass. What is the ratio of the gravitational force between Objects A and B to the gravitational force between Objects B and C? (1 point)
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Answer 1

Let the distance AC = CB = r, so AB = 2r. Let mA = mB = m and mC = m/3. Then

F_AB = G m*m / (2r)^2 = G m^2 / (4r^2)
F_BC = G m*(m/3) / r^2 = G m^2 / (3r^2)

Ratio F_AB / F_BC = (1/4) / (1/3) = 3/4.

So the ratio is 3/4 (or 3:4).