Having landed on a newly discovered planet, an astronaut sets up a simple pendulum of length 1.25 m and finds that it makes 419 complete osc

Question

Having landed on a newly discovered planet, an astronaut sets up a simple pendulum of length 1.25 m and finds that it makes 419 complete oscillations in 1230 s. The amplitude of the oscillations is very small compared to the pendulum’s length. What is the gravitational acceleration on the surface of this planet?

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Khải Quang 5 months 2021-08-04T20:24:25+00:00 1 Answers 7 views 0

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    2021-08-04T20:26:08+00:00

    Answer:

    g=2406.8m/s^{2}

    Explanation:

    firstly we have to find the frequency and then the angular frequency.

    The frequency will be:

       f=\frac{419}{60} \\f=6.98Hz

    The angular frequency is:

    ω=2\pi f

    ω=2*\frac{22}{7} *6.98

    ω=43.88rad /sec

    Now we can apply simple pendulum relationship

    ω=\sqrt{\frac{g}{l} }

    make g the subject of the formula

    g=w^{2} l\\g=43.88^{2} *1.25\\g=2406.8m/s^{2}

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