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Speed or height from conservation of gravitational energy over large heights

This type of question, asked 5 times: 26 Jul 2022, 27 Jul 2022, 30 Jan 2023, 15 Apr 2023, 2 Apr 2026 S2. All 5 questions below, oldest first.

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  1. Question 1

    26 Jul 2022

    98
    A body is projected vertically upwards from the surface of earth with a velocity equal to one third of escape velocity. The maximum height attained by the body will be: (Take radius of earth =6400 km= 6400\text{ }km and g=10 ms−2g = 10{\text{ }ms}^{- 2} )

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  2. Question 2

    27 Jul 2022

    96
    A body of mass mm is projected with velocity λve\lambda v_{e} in vertically upward direction from the surface of the earth into space. It is given that vev_{e} is escape velocity and λ<1\lambda < 1. If air resistance is considered to the negligible, then the maximum height from the centre of earth, to which the body can go, will be ( RR : radius of earth)

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  3. Question 3

    30 Jan 2023

    104
    An object is allowed to fall from a height RR above the earth, where RR is the radius of earth. Its velocity when it strikes the earth's surface, ignoring air resistance, will be

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  4. Question 4

    15 Apr 2023

    10
    A body is released from a height equal to the radius (R) of the earth. The velocity of the body when it strikes the surface of the earth will be: (Given g=g = acceleration due to gravity on the earth.)

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  5. Question 5

    2 Apr 2026 S2

    6
    If a body of mass 1 kg falls on the earth from infinity, it attains velocity (v) and kinetic energy (k) on reaching the surface of earth. The values of v and k respectively are ____\_\_\_\_ . (Take radius of earth to be 6400 km and g=9.8 m/s2g = 9.8\text{ }m/s^{2} )

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