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Time period or length of a pendulum at a height above the earth

This type of question, asked 6 times: 25 Jul 2022, 28 Jul 2022, 25 Jan 2023, 30 Jan 2024, 1 Feb 2024, 5 Apr 2024. All 6 questions below, oldest first.

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  1. Question 1

    25 Jul 2022

    103
    The length of a seconds pendulum at a height h=2Rh = 2R from earth surface will be: (Given: R=R = Radius of earth and acceleration due to gravity at the surface of earth g=π2 m/s−2g =\pi^{2}\text{ }m/s^{- 2} )

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  2. Question 2

    28 Jul 2022

    96
    Assume there are two identical simple pendulum Clocks-1 is placed on the earth and Clock-2 is placed on a space station located at a height hh above the earth surface. Clock-1 and Clock-2 operate at time periods 4 s4\text{ }s and 6 s6\text{ }s respectively. Then the value of hh is (consider radius of earth RE=6400 kmR_{E}= 6400\text{ }km and gg on earth 10 m/s210\text{ }m/s^{2} )

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  3. Question 3

    25 Jan 2023

    20
    TT is the time period of simple pendulum on the earth's surface. Its time Period becomes xTxT when taken to a height RR (equal to earth's radius) above the earth's surface. Then, the value of xx will be:

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  4. Question 4

    30 Jan 2024

    118
    A simple pendulum is placed at a place where its distance from the earth's surface is equal to the radius of the earth. If the length of the string is 4 m4\text{ }m, then the time period of small oscillations will be _____ s. (take g=π2 ms−2g = \pi^{2}{\text{ }ms}^{- 2})

  5. Question 5

    1 Feb 2024

    2
    If RR is the radius of the earth and the acceleration due to gravity on the surface of earth is g=π2 m/s2g=\pi^{2}\text{ }m/s^{2}, then the length of the second's pendulum at a height h=2Rh= 2R from the surface of earth will be,

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  6. Question 6

    5 Apr 2024

    15
    A simple pendulum doing small oscillations at a place RR height above earth surface has time period of T1=4 sT_{1}= 4\text{ }s. T2T_{2} would be it's time period if it is brought to a point which is at a height 2R2R from earth surface. Choose the correct relation [R=\lbrack R = radius of Earth]:

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