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")=mgh, W_("ext")=(m) ((GM_(e))/R_(e)^(2))(R_(e)/1000)=(GM_(e)m)/(1000 R_(e))`
(ii) `h=R_(e)`, in this case h is not very less than `R_(e)`, so we cannot apply `Delta U= mgh`
`W_("ext")=U_(f)-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))`