A thin hoop is supported in a vertical plane by a nail. What should the radius of the hoop be in order for it to have a period of oscillatio

Question

A thin hoop is supported in a vertical plane by a nail. What should the radius of the hoop be in order for it to have a period of oscillation of 1.00 s

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Mộc Miên 4 years 2021-08-21T05:14:36+00:00 1 Answers 25 views 0

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  1. King
    0
    2021-08-21T05:16:07+00:00
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    Answer:

    0.124 m

    Explanation:

    the period of a simple pendulum with a small amplitude is given as

    T = 2π [√(I/mgd)]

    From the above stated formula,

    I = moment of inertia

    m = mass of the pendulum

    g = acceleration due to gravity, 9.8 m/s²

    d = distance from rotation axis due to center of gravity

    Also, moment of Inertia, I = 2mr², if we substitute this in the above formula, we have

    T = 2π [√(2mr²/mgd)]

    If we assume that our r = d, then we have

    T = 2π [√(2r/g)]

    If we make r the subject of the formula in the above equation, we get

    r = gT² / 8π²

    r = (9.8 * 1²) / 8 * π²

    r = 9.8 / 78.98

    r = 0.124 m

    Thus, the radius of the hoop is 0.124 m

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