After landing on an unfamiliar planet, a space explorer constructs a simple pendulum of length 54.0 cm. The explorer finds that the pendulum

Question

After landing on an unfamiliar planet, a space explorer constructs a simple pendulum of length 54.0 cm. The explorer finds that the pendulum completes 98.0 full swing cycles in a time of 135s.

Required:
What is the value of g on this planet?

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Ngọc Diệp 4 weeks 2021-08-17T12:55:58+00:00 1 Answers 2 views 0

Answers ( )

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    2021-08-17T12:56:58+00:00

    Answer:

    g = 11.2 m/s²

    Explanation:

    First, we will calculate the time period of the pendulum:

    T = \frac{t}{n}

    where,

    T = Time period = ?

    t = time taken = 135 s

    n = no. of swings in given time = 98

    Therefore,

    T = \frac{135\ s}{98}

    T = 1.38 s

    Now, we utilize the second formula for the time period of the simple pendulum, given as follows:

    T = 2\pi \sqrt{\frac{l}{g}}

    where,

    l = length of pendulum = 54 cm = 0.54 m

    g = acceleration due to gravity on the planet = ?

    Therefore,

    (1.38\ s)^2 = 4\pi^2(\frac{0.54\ m}{g} )\\\\g = \frac{4\pi^2(0.54\ m)}{(1.38\ s)^2}

    g = 11.2 m/s²

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