The earth\'s acceleration due the gravity varies from 9.78 m/s2 at the equator t

Question

The earth's acceleration due the gravity varies from 9.78 m/s2 at the equator to 9.83 m/s2 at the poles. A pendulum whose length is precisely 1.000 m can be used to measure g. Such a device is called a gravimeter. (a) How long do 100 oscillations take at the equator? s (b) How long do 100 oscillations take at the north pole? s (b) Suppose you take your gravimeter to the top of a high mountain peak near the equator. There you find that 100 oscillations take 201.1 seconds. What is g on the mountain top?

Explanation / Answer

You should simply apply the pendulum period formula: T = 2pv(L/g) a. L = 1.000 m, g = 9.78 m/s² T = 6.283 v(1.000 / 9.78) = 2.009 s 100 T = 200.9 s B) L = 1.000 m, g = 9.83 m/s² T = 6.283 v(1.000 / 9.83) = 2.004 s 100 T = 200.4 s C) 100 T = 201 s T = 2.01 s g = 4p²L / T² = 4 * 3.1416² * 1.000 / 2.01² = 9.77 m/s²

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