The equation derived in Problem 17 is nonlinear, but for small 0 it is customary to approximate it by the equation

Here g = GM / R2, where G is a universal constant, M is the mass of the earth, and R is the distance from the pendulum to the center of the earth. Two clocks, with pendulums of length L1 and L2 and located at distances R1 and R2 from the center of the earth, have periods pt and the, p1 and p2, respectively.
(a) Show that

(b) Find the height of a mountain if a clock that kept perfect time at sea level (R = 3960 miles) with L = 81 inches had to have its pendulum shortened to L = 80.85 inches to keep perfect time at the top of the mountain.

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