Physics

On planet e a pendulum has a length of 4L has a period of 6T, on planet F a pendulum has a length of 3L has a period of 2T what is the ratio of gravitational acceleration of these two planets

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  1. since T = 2π√(L/g), g = (4π^2L)/T^2
    the ratio of
    g1/g2 = (4π^2L1)/(T1^2) / (4π^2L2)/T2^2
    = (4L)/(6T)^2 / (3L)/(2T)^2
    = (4/36) / (3/4)
    = 1/9 * 4/3
    = 4/27

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  2. g=4π^2L/T^2

    So,

    gF/gE=(4π^2L/T^2)/(4π^2L/T^2)=(4π^2(3L)/(2T)^2)/(4π^2(4L)/(6T)^2)

    gF/gE=(4π^2(3L)/(2T)^2)/(4π^2(4L)/(6T)^2)=(3L/4T^2)/(4L/36T^2)

    gF/gE=(3L/4T^2)/(4L/36T^2).

    gF/gE=(3/4)*9=27/4=6.75

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