At sea level, at a latitude where , a pendulum that takes 2.00 s for a complete swing back and forth has a length of 0.993 m. What is the va

Question

At sea level, at a latitude where , a pendulum that takes 2.00 s for a complete swing back and forth has a length of 0.993 m. What is the value of g in m/s2 at a location where the length of such a pendulum is 0.970 m

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Dulcie 3 years 2021-08-09T17:29:15+00:00 1 Answers 43 views 0

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  1. Gerda
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    2021-08-09T17:30:48+00:00
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    Answer:

    a) The value of g at such location is:

    g=9.8005171\,\frac{m}{s^2}

    b) the period of the pendulum with the length is 0.970 m is:

    T=1.9767 sec

    Explanation:

    Recall the relationship between the period (T) of a pendulum and its length (L) when it swings under  an acceleration of gravity g:

    L=\frac{g}{4\,\pi^2} \,T^2

    a) Then, given that we know the period (2.0 seconds), and the pendulum’s length (L=0.993 m), we can determine g at that location:

    g=\frac{4\,\pi^2\,L}{T^2}\\g=\frac{4\,\pi^2\,0.993}{(2)^2}\\g=\pi^2\,(0.993)\,\frac{m}{s^2} \\g=9.8005171\,\frac{m}{s^2}

    b) for this value of g, when the pendulum is shortened to 0.970 m, the period becomes:

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