An object is thrown vertically upwards from the surface of the earth with a velocity x times the escape velocity on the earth `(x lt 1)`, then the maximum height ot which its rises from the centre of the earth is (radius of earth is R)

Options

A. `R(1-x)^2`
B. `( R)/(1-x^2)`
C. `(1-x^2)/( R)`
D. `(x^2)/(1- R)`

Explanation

(No option is matching )
Escape velocity is `v_e= sqrt(2GM)/(R )`
Let object rises upto height h when it is thrown with speed `x.v_e` , then from conservtion of energy, we get
`1/2 m(x.v_e)^2-(GMm)/(R )=0- (GMm)/(R+h)`

`rArr 1/2m(x.v_e)= (GMm)/(R )- (GMm)/(R+h)`
`rArr (x-v_e)^2 = 2GM (h)/(R+h)`
`rArr x^2 = (h)/(R+h) or h= (Rx^2)/(1-x^2)`