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 `nlt1`. Neglecting air resistance, to what height will the ball rise? (Take radius of the earth=R):-

Options

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

Answer

C

Explanation

`1/2mv^(2)=(GMm)/R-(GMm)/(R+h)`
`=(GMmh)/(R(R+h))`
`:.1/2mv^(2)=(mghR)/(R+h)`
Since `v=nv_(e)` and `v_(e)=sqrt(2gR)`
hence `h=(Rn^(2))/((1-n^(2)))`