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A small mass m is moved slowly from the ...

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

A

mgh, for all values of h

B

mgh, for `h lt lt R`

C

`1//2` mgR for h=R

D

`-1//2`mgR for h=R

Text Solution

Verified by Experts

The correct Answer is:
B, C
`W=U_(2)-U_(1)=(GM m)/(R+h)-(-(GM m)/(R ))`
`=-GM m((1)/(R )-(1)/(R+h))=gR^(2)m[(h)/(R(R+h))]=(mgRh)/(R+h)`
For `h lt lt R`, W=mgh,
For h=R, `W=(mgR)/(2)`
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