1.

A ball of mass m is fired vertically upwards from the surface of the earth with velocity nv_​e​, where v_​e is the escape velocity and n < 1. Neglecting air resistance, to what height will the ball rise ? (Take radius of the earth as R) :-

Answer»

`R//n^2`
`R//(1-n^2)`
`Rn^2//(1-n^2)`
`Rn^2`

Solution :`1/2mv^2 = (GMN)/R -(GMn)/(R+H)`
`=(GMmh)/(R(R+h))`
`THEREFORE 1/2 mv^2 =(mghR)/(R+h)`
Since , `v=nv_e` and `v_e=sqrt(2gR)` ,
HENCE `h=(Rn^2)/((1-n^2))`


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