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Answer to Question #5570 in Mechanics | Relativity for alex

Question #5570
a visitor to a lighthouse wishes to determine the height of the tower. she ties a spool of thread to a small rock to make a simple pendulm, which she hangs down the center of a spiral staircase of the tower. The period of oscillation is 10.8s. The acceleration of gravity is 9.8 m/s. What is the height? Answer in units of m
Expert's answer
The period of oscillation of a pendulum is given by the following formula
data:image/png;base64,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
Hence we get the value of height
data:image/png;base64,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
Answer: 29m

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