Answer
We can rank the arrangements according to the magnitude of the net gravitational force on the central particle due to the other three particles:
$(c) \gt (b) \gt (a)$
Work Step by Step
Let $M$ be the mass of each particle.
We can find the magnitude of the gravitational force on the central particle from each of the three other particles:
$F = G~\frac{(M)(M)}{r^2} = \frac{GM^2}{r^2}$
When we find the net gravitational force on the central particle from the three other particles, we need to add the three gravitational forces as a vector sum.
The vector sum of the three gravitational forces on the central particle is maximized when the three forces act in the same direction, and minimized when the forces act in opposite directions.
We can rank the arrangements according to the magnitude of the net gravitational force on the central particle due to the other three particles:
$(c) \gt (b) \gt (a)$
