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

Explanation

For a platform at a height h,
escape energy = binding energy of sphere
`rArr (1)/(2)mv'._(e)^(2)=(GMm)/(R+h)rArrv'_(e)=sqrt((2GM)/(R+h))=sqrt((2GM)/(2R))" "(because h=R)`
But at surface of earth, `v_(e)=sqrt((2GM)/(R))`
As given, `v'_(e)=fv_(e)`
Hence, `sqrt((2GM)/(2R))=fsqrt((2GM)/(R))or (1)/(2R)=(f^(2))/(R)rArr f=(1)/(sqrt(2))`.