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Speed or kinetic energy of a body falling towards the earth from a large height

This type of question, asked 4 times: 10 May 2023 S2, 11 May 2024 S1, 14 May 2024 S2, 19 May 2026 S1. All 4 questions below, oldest first.

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  1. Question 1

    10 May 2023 S2

    24
    A body starts from rest from a distance R0R_0 from the centre of the earth. The velocity acquired by the body when it reaches the surface of the earth will be (R = radius of earth, M = mass of earth)

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  2. Question 2

    11 May 2024 S1

    35
    A body of mass m kg starts falling from a distance 3R above earth's surface. When it reaches a distance R above the surface of the earth of radius R and mass M, then its kinetic energy is

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  3. Question 3

    14 May 2024 S2

    6
    A body starts its motion from rest from a point distant R0R_0 (R0>RR_0 > R) from the centre of the earth. The velocity acquired by the body when it reaches the surface of earth will be (GG = universal constant of gravitation, MM = mass of earth, RR = radius of earth)

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  4. Question 4

    19 May 2026 S1

    109
    A body of mass 'm' is raised to a height '10R10R' from the surface of the earth, where 'R' is the radius of the earth. Suppose it is released now. The speed with which it will strike the surface of the earth is nearly [gg = acceleration due to gravity]

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