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Period of a satellite orbiting close to a planet's surface in terms of density

The same question, asked 4 times: May 2021 S1, 9 May 2023 S2, 16 May 2023 S1, 19 Apr 2026 S2. Every wording below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    May 2021 S1

    36
    A satellite is revolving round a planet in a circular orbit close to its surface. ρ\rho is mean density and RR is the radius of planet. The period is (GG = universal constant of gravitation)

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  2. Question 2

    9 May 2023 S2

    22
    A satellite is revolving around a planet in a circular orbit close to its surface. Let 'ρ\rho' be the mean density and 'R' be the radius of the planet. Then the period of the satellite is (G = universal constant of gravitation)

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  3. Question 3

    16 May 2023 S1

    34
    A satellite is orbiting just above the surface of the planet of density 'ρ\rho' with periodic time 'T'. The quantity T2ρT^2\rho is equal to (G=G = universal gravitational constant)

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  4. Question 4

    19 Apr 2026 S2

    108
    A satellite is revolving around a planet in a circular orbit close to its surface. Let ρ\rho be mean density and RR be the radius of the planet; then the period of the satellite is (GG = Universal constant of gravitation).

    Tap an option to check your answer.