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3 February, 19:10

2. One of two identical grandfather pendulum clocks from Earth is placed on Mars. If the grandfather clock on Mars is 23 minutes behind the grandfather clock on Earth after 1 hour, what is the acceleration due to gravity on Mars

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  1. 3 February, 20:40
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    Acceleration due to gravity on Mars = 3.72 m/s²

    Explanation:

    It is given that the grandfather clock on Mars lags 23 minutes behind the grandfather clock on Earth after 1 hour.

    Mars = 60 - 23 = 37 minutes

    So the time on Mars is 37 minutes when time on Earth is 60 minutes.

    We know that time period on Earth is given by

    Te = 2π√ (L/ge)

    Where ge is acceleration due to gravity on the Earth

    We know that time period on Mars is given by

    Tm = 2π√ (L/gm)

    Where gm is acceleration due to gravity on the Mars

    So,

    Te/Tm = 37/60 = 0.616

    0.616 = 2π√ (L/ge) / 2π√ (L/gm)

    Simplifying the above equation yields

    0.616 = √gm/√ge

    √gm = √ge*0.616

    squaring on both sides

    gm = ge*0.616²

    The acceleration on the Earth is 9.81 m/s²

    gm = 9.81*0.616²

    gm = 3.72 m/s²

    Therefore, the acceleration due to gravity on Mars is 3.72 m/s².
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