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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:

","answerCount":1,"acceptedAnswer":{"@type":"Answer","text":"

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 $PE$

$$\\therefore W = U_f - U_i$$

$$\\frac{GMm}{2R} = \\frac{gR^2 m}{2R} = \\frac{mgR}{2} \\quad (GM = gR^2)$$

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