g = G*M / r^2, where g is the gravitational field strength, G is the gravitational constant, M is the mass of the attracting body, r is the distance from the center of mass of the body.
V = -G*M / r, where V is the gravitational potential.
The Attempt at a Solution
For the gravitational field strength, as P is at a midpoint, we can say that r is 1/2*r, and as the masses are also equal, G*M / 1/2*r^2 = G*M / 1/2*r^2 (as they are equal, and in opposite directions), and they will simply cancel to 0. Therefore, it can't be A or B.
For gravitational potential, again, the masses are equal, and r is 1/2*r, so -GM / 1/2*r = -GM / 1/2*r, they will again cancel to 0. However, the answer is apparently C, where gravitational potential is -4G*M / r? I can't see why.