The amount of work done to raise a mass ' $m$ ' from the surface of the Earth to a height equal to t

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The amount of work done to raise a mass ' $m$ ' from the surface of the Earth to a height equal to the radius of the Earth ' $R$ ' will be

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Sol. [Key Concept: Gravitation — work to raise mass to height h=R] W.D. $= U_{2} - U_{1}$$$\begin{matrix} & \ = - \frac{GMm}{R + R} - \left( \frac{- GMm}{R} ight) \ & \ = - \frac{GMm}{2R} + \frac{GMm}{R} \ & \ = \frac{GMm}{2R} = \frac{mgR}{2} \end{matrix}$$

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