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

`rArr (1)/(2) mv^(2)=(GMm)/(R )-(GMm)/(R+h)=(GMmh)/(R(R+h))`
`rArr therefore (1)/(2) mv^(2)=(mghR)/(R+h)`
since `v=nv_(e) ` and `v_(e)=sqrt(2gR)`,
hence `h=(Rn^(2))/(1-n^(2))`