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A body of mass m is placed on the surfac...

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)`

Text Solution

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(i). `h=(R_(e))/(1000)` as `hltltR_(e)` so we apply `W_(ext)=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 less than `R_(e)` so we cannot apply `DeltaU=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))`
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