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A large pendulum with a 200-lb gold plated bob 12 inches in diameter is on display in the lobby of the United Nations building. The pendulum has a length of 75 ft. It is used to show the rotation of the Earth—for this reason it is referred to as a Foucault pendulum.Part A) If the pendulum were to be taken to the Moon, where the acceleration of gravity is g/6, would the period increase, decrease, or stay the same?

Part B) Check your result in part A by calculating the period of the pendulum on the Moon.

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Answer:

9.59143 s

23.4941 s

Explanation:

L = Length of pendulum = 75 ft

g = Acceleration due to gravity = 9.81 m/s²

Time period is given by

[tex]T=2\pi \sqrt{\dfrac{L}{g}}[/tex]

On Earth

[tex]T=2\pi \sqrt{\dfrac{75\times 0.3048}{9.81}}\\\Rightarrow T=9.59143\ s[/tex]

The time period on Earth is 9.59143 s

On Moon

[tex]T=2\pi \sqrt{\dfrac{75\times 0.3048}{\dfrac{9.81}{6}}}\\\Rightarrow T=23.4941\ s[/tex]

The time period on Moon is 23.4941 s

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