The earth\'s free-fall acceleration varies from 9.78 m/s2 at the equator to 9.83

Question

The earth's free-fall acceleration varies from 9.78 m/s2 at the equator to 9.83 m/s2 at the poles, both because the earth is rotating and it's not a perfect sphere. A pendulum whose length is precisely 1.000 m can be used to measure g . Such a device is called a gravimeter

Part A

How long do 165 oscillations take at the equator?

Part B

How long do 165 oscillations take at the north pole?

Part C

Is the difference between your answers to parts a and b measurable?(Yes or no)

What kind of instument could you use to measure the difference?

Part E

Suppose you take your gravimeter to the top of a high mountain peak near the equator. There you find that 100 oscillations take 201.0 s. What is g on the mountain top?

Explanation / Answer

You should simply apply the pendulum period formula:
T = 2(L/g)

A) L = 1.000 m, g = 9.78 m/s²
T = 6.283 (1.000 / 9.78) = 2.009 s
165T = 331.485 s

B) L = 1.000 m, g = 9.83 m/s²
T = 6.283 (1.000 / 9.83) = 2.004 s
165 T = 330.66 s

C) difference between parts a and b = 0.825 s =825 ms (Yes, it is measurable)

E) 100 T = 201 s
T = 2.01 s
g = 4²L / T² = 4 * 3.1416² * 1.000 / 2.01² = 9.77 m/s²

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