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Period of a pendulum at a height above the earth

This type of question, asked 3 times: 9 May 2024 S1, 16 Apr 2026 S2, 18 Apr 2026 S1. All 3 questions below, oldest first.

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  1. Question 1

    9 May 2024 S1

    1
    A seconds pendulum is placed in a space laboratory orbiting round the earth at a height '3R3R' from the earth's surface. The time period of the pendulum will be (R=R= radius of earth)

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  2. Question 2

    16 Apr 2026 S2

    120
    The time taken by simple pendulum for one oscillation is T on earth's surface. Its time period becomes xT when taken to a height R (equal to earth's radius) above the earth's surface. The value of x is

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  3. Question 3

    18 Apr 2026 S1

    108
    The lengths of seconds pendulums on the surface of the earth and at an altitude 'hh' from the surface of the earth are lsl_s and lhl_h respectively. The radius of the earth is

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