Three particles, two with mass m and one mass M, might be arranged in any of the four configurations known below.Rank the configurations according to the magnitude of the gravitational force on M, least to greatest.
A)1, 2, 3, 4
B)2, 1, 3, 4
C)2, 1, 4, 3
D)2, 3, 4, 2
E)2, 3, 2, 4

Question

Three particles, two with mass m and one mass M, might be arranged in any of the four configurations known below.Rank the configurations according to the magnitude of the gravitational force on M, least to greatest. 
A)1, 2, 3, 4 
B)2, 1, 3, 4 
C)2, 1, 4, 3 
D)2, 3, 4, 2 
E)2, 3, 2, 4

Quizplus · Accepted Answer

The magnitude of the gravitational force on M depends on the masses of the other particles and their distances from M. In configurations 1, 2, and 3, M is the same distance away from the two particles with mass m, so the magnitude of the gravitational force on M in these configurations will depend only on the mass of the particle M and the mass of one of the particles with mass m. 
In configuration 1, M is the farthest away from the particle with mass M, so the magnitude of the gravitational force on M will be the least. 
In configuration 2, M is equidistant from the two particles with mass m and closest to the particle with mass M, so the magnitude of the gravitational force on M will be greater than in configuration 1. 
In configuration 3, M is closest to the particle with mass M, so the magnitude of the gravitational force on M will be greater than in configuration 2. 
In configuration 4, all three particles are equidistant from M, so the magnitude of the gravitational force on M will depend on the masses of all three particles. The mass of the particle with mass M is greater than the mass of the other two particles combined, so the magnitude of the gravitational force on M will be the greatest in this configuration.

Three Particles, Two with Mass M and One Mass M