A small mass `m` is moved slowly from the surface of the earth to a height `h` above the surface. The work done (by an external agent) in doing this is

Options

A. `mgh`, for all values of h
B. `mgh`, for `hlt ltR`
C. `1//2, mgR`, for `h=R`
D. `-1//2mgR`, for `h=R`

Answer

B, C

Explanation

`W=U_(2)-U_(1)=(GMm)/(R+h)(-(GMm)/R)=-GMm[1/R-1/(R+h)]`
`=gR^(2)m[h/(R(R+h))]=(mgRH)/(R+h)`
For `hlt ltR, W=mgh`
for `h=R, W=(mgR)/2`