Alphymus

Two small, equal masses are attached by a lightweight rod. This object orbits a planet; the length of the rod is smaller than the radius of the orbit, but not negligible. The rod rotates about its axis in such a way that it remains vertical with respect to the planet.

Is there a force in the rod? If so, is it tension or compression?

Is the equilibrium stable, unstable, or neutral with respect to a small perturbation in the angle of the rod? (Assume this perturbation maintains the rate of rotation, so that in the co-rotating frame the rod is still stationary but at an angle to the vertical.)

(A) There is no force in the rod; the equilibrium is neutral.
(B) The rod is in tension; the equilibrium is stable.
(C) The rod is in compression; the equilibrium is stable.
(D) The rod is in tension; the equilibrium is unstable.
(E) The rod is in compression; the equilibrium is unstable.