Physics I need help

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? 

A) 3/4

B) 3

C) 3/2

D) 2

Answer 1

Let

r be the distance from A to C as well as distance from B to C,

m be the mass of C,

G be the gravitational constant.

Then the distance from A to B is 2r.

The mass of both A and B is 3m.

The gravitational force between A and B is

G×3m×3m/(2r)² = 9Gm²/4r²

The gravitational force between B and C is

G×m×3m/r² = 3Gm²/r²

You can calculate the ratio between the two forces.