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Time period or frequency of a pendulum where g changes (height, depth, another planet)

This type of question, asked 7 times: 4 May 2023 S2, 16 May 2023 S1, 10 May 2024 S1, 12 May 2024 S1, 12 May 2024 S2, 22 Apr 2025 S1, 18 Apr 2026 S1. All 7 questions below, oldest first.

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  1. Question 1

    4 May 2023 S2

    21
    A pendulum is oscillating with frequency 'n' on the surface of earth. If it is taken to a depth R4\frac{R}{4} below the surface of earth, new frequency of oscillation at depth R4\frac{R}{4} is (R=R = radius of earth)

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  2. Question 2

    16 May 2023 S1

    42
    A simple pendulum has a periodic time 'T1T_1', when it is on the surface of earth of radius 'R'. Its periodic time is 'T2T_2' when it is taken to a height 'R' above the earth's surface. The value of T2T1\frac{T_2}{T_1} is

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  3. Question 3

    10 May 2024 S1

    42
    There is a second's pendulum on the surface of earth. It is taken to the surface of planet whose mass and radius are twice that of earth. The period of oscillation of second's pendulum on the planet will be

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  4. Question 4

    12 May 2024 S1

    14
    Time period of simple pendulum on earth's surface is TT. 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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  5. Question 5

    12 May 2024 S2

    38
    A simple pendulum is oscillating with frequency F on the surface of the earth. It is taken to a depth below the surface of earth (R=R = radius of earth). The frequency of oscillation at depth R/3R/3 is

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  6. Question 6

    22 Apr 2025 S1

    33
    Time period of a simple pendulum on earth's surface is ' T '. It time period becomes ' xT ' when taken to a height ' 2R2R ' above earth's surface. The value of xx will be ( R=R= radius of earth)

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  7. Question 7

    18 Apr 2026 S1

    109
    Time period of a simple pendulum is T1T_1 when on the earth's surface and T2T_2 when taken to a height '2R' above the earth's surface, where 'R' is the radius of the earth. The ratio T1:T2T_1 : T_2 is

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