Chapter 6, Problem 17P

(II) Two identical point masses, each of mass M, always remain separated by a distance of 2R. A third mass m is then placed a distance x along the perpendicular bisector of the original two masses, as shown in Fig. 6–26. Show that the gravitational force on the third mass is directed inward along the perpendicular bisector and has a magnitude of and has a magnitude of

$F=\frac{2GMmx}{{(x^2+R^2)}^{\frac{3}{2}}}.$

FIGURE 6-26

Problem 17.