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  4. The work done to raise a mass m from the surface of the earth to a height h. which is equal to the radius of the earth, is :

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Q. The work done to raise a mass $m$ from the surface of the earth to a height $h$. which is equal to the radius of the earth, is :

NEETNEET 2019Gravitation

Solution:

Initial potential energy at earths surface is
$U_i = \frac{-GMm}{R}$
Final potential energy at height h = R
$U_{f} = \frac{-GMm}{2R} $
As work done = Change in PE
$ \therefore W = U_{f} -U_{i} $
$ = \frac{GMm}{2R} = \frac{gR^{2}m}{2R} = \frac{mgR}{2} \left(\because GM = gR^{2}\right) $

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