The earth is assumed to be a sphere of raduis `R`. A plateform is arranged at a height `R` from the surface of the `fv_(e)`, where `v_(e)` is its escape velocity form the surface of the earth. The value of `f` is

Options

A. `1//3`
B. `1//2`
C. `sqrt(2)`
D. `1//sqrt(2)`

Answer

C

Explanation

`1/2 mv_(p)^(2)-(GMm)/(R+R)=0 implies v_(p)=sqrt((GM)/R)`
`(v_(p))/(v)=sqrt(2) implies v_(p)=sqrt(2)v_(e)=sqrt(2)v=fv`
`f=sqrt(2)`