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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 :
(i) mgh, for h << R
(ii) mgh, for all values of h
$(iii) \frac{mgR}{2}, for h = R$
$(iv) - \frac{mgR}{2}, for h = R$

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(i, iii)

(i, iii, iv)

(ii, iii)

(i, ii)

answer is B.

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Detailed Solution

If h <<< R,W $= ΔU = mgh$
If h = R,w $= ΔU = - \frac{GMm}{(2 R)} - (- \frac{GMm}{R}) = \frac{GMm}{2 R} = \frac{mgR}{2}$

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