A thin, uniform rod has length L and mass M.A small uniform sphere of mass m is placed a distance x from one end of the rod, along the axis of the rod (Figure 1). Flgure < 1 of 1 M m. Part A Caiculate the gravitational potential energy of the rod-sphere system. Take the polential energy lo be zera when Ihe rod and sphere are infinitely far apart. (Hint: Use the power series expansion for lIn(1+r).) Express your answer in terms of m, M, L, x, G. ? U = Part B Use F = -dU /dx to find the magnitude of the gravitational force exerted on the sphere by the rod. Express your answer in terms of m, M, L, x, G. ? F = Part C Find the direction of the gravitational force exerted on the sphere by the rod. the force is directed to the rod the force is directed out of the rod