Question: A thin disk of radius a and mass M lies horizontally; a particle of mass m is at a height h directly above the center of the disk. The gravitational force, F, exerted by the disk on the mass m is given by
F = ((2GMmh)/a2)((1/h) - (1/(a2 + h2)1/2)
where G is a constant. Assume a
(b) Show that the approximation for F obtained by using only the first nonzero term in the series is independent of the radius, a.
(c) If a = 0.02h, by what percentage does the approximation in part (a) differ from the approximation in part (b)?