Answer
We can rank the arrangements according to the gravitational potential energy of the four-particle system, with the least negative first:
$(a) \gt (b) \gt (c)$
Work Step by Step
Let $M$ be the mass of each particle.
We can write the expression for the gravitational potential energy in a system of two particles:
$U = -\frac{G~M^2}{r}$
To find the total potential energy in a system of four particles, we need to sum the gravitational potential energy for each pair of particles.
Note that as the distance $r$ between the particles increases, then the value of $U$ becomes less negative.
We can rank the arrangements according to the gravitational potential energy of the four-particle system, with the least negative first:
$(a) \gt (b) \gt (c)$
