Mass M is distributed uniformly over a disk of radius a. Find the gravitational force (magnitude and direction) between this disk-shaped mass and a particle with mass m located a distance x above the center of the disk (Fig. 12.39). Does your result reduce to the correct expression as x becomes very large? (Hint: Divide the disk into infinitesimally thin concemric rings, use the expression derived in Exercise 12.41 for the gravitational force due to each ring, and integrate to find the total force.)