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CALC 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. P13.81). Does your result reduce to the correct expression as x becomes very large? (Hint: Divide the disk into infinitesimally thin concentric rings, use the expression derived in Exercise 13.35 for the gravitational force due to each ring, and integrate to find the total force.)
Figure P13.81
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