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Body projected upward with a fraction of the escape velocity: maximum height reached

The same question, asked 2 times: 26 Jul 2022*, 27 Jul 2022. Every wording 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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