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Maximum height reached by a body projected with a fraction of escape velocity

This type of question, asked 7 times: 11 May 2023 S2, 10 May 2024 S2, 12 May 2024 S2, 20 Apr 2025 S1, 13 Apr 2026 S1, 12 May 2026 S2, 15 May 2026 S2. All 7 questions below, oldest first.

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  1. Question 1

    11 May 2023 S2

    28
    A body is projected in vertically upward direction from the surface of the earth of radius 'R' into space with velocity 'nVe' (n<1)(n<1). The maximum height from the surface of earth to which a body can reach is

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  2. Question 2

    10 May 2024 S2

    43
    A body is projected vertically from earth's surface with velocity equal to half the escape velocity. The maximum height reached by the satellite is (R=R= radius of earth)

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  3. Question 3

    12 May 2024 S2

    44
    A body is projected vertically upwards from earth's surface of radius 'RR' with velocity equal to 13\frac{1}{3}rd of escape velocity. The maximum height reached by the body

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  4. Question 4

    20 Apr 2025 S1

    33
    A body is projected vertically from earth's surface with (13)rd \left( \frac{1}{3} \right)^{\text{rd~}} of escape velocity. The maximum height reached by the body is ( R=R = radius of earth)

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  5. Question 5

    13 Apr 2026 S1

    109
    A body is projected vertically from earth's surface of radius R with velocity equal to half the escape velocity. The maximum height reached by the body is

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  6. Question 6

    12 May 2026 S2

    107
    A body is projected vertically upwards from earth's surface. If its kinetic energy of projection is equal to half of its minimum value required to escape from the gravitational influence then the height up to which it rises is (RR = radius of earth)

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  7. Question 7

    15 May 2026 S2

    109
    A particle of mass mm is projected with a velocity v=KVe (K<1)v = KV_e\ (K < 1) from the surface of the earth. The maximum height above the surface reached by the particle is (VeV_e = escape velocity, RR is radius of earth)

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