The acceleration due to gravity g varies with geographical location because of the earth’s rotation and because the earth is not exactly spherical. This was first discovered in the seventeenth century, when it was noted that a pendulum clock carefully adjusted to keep correct time in Paris lost about 90 s per day near the equator.

(a) Show that a small change in the acceleration of gravity ∆g produces a small change in the period ∆T of a pendulum given by.

(Use differentials to approximate ∆T and ∆g.)

(b) How great a change in g is needed to account for a change in the period of 90 s per day?

Ag 2 g