A body of mass m is placed on the surface of earth. Find work required to lift this body by a height
(i). `h=(R_(e))/(1000)`
(ii). `h=R_(e)`

Explanation

(i) `h = (R_(e))/(1000)` as `h lt lt R_(e)`. so
we can apply
`W_(ext) U uarr = mgh`
`W_(ext)= (m) ((GM_(e))/(R_(e)^(2))) ((R_(e))/(1000)) = (GM_(e)m)/(1000R_(e))`
(ii) `h =R_(e)` in this case h is not very iess than `R_(e)` so we cannot apply `DeltaU = mgh`
so we cannot apply `DeltaU = mgh`
`W_(ext) = U uarr = U_(i) = m (V_(f) - V_(i))`
`W_(ext) = m[(- (GM_(e))/(R_(e)+R_(e))) - (- (GM_(e))/(R_(e)))]`
`W_(ext) = - (GM_(e)m)/(2R_(e))` .