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 :

Question

TestHub · Accepted Answer

Initial potential energy at the surface of the Earth is $U_{i} = - \frac{GM m}{R}$

Final potential energy at height $h = R$ is $U_{f} = - \frac{GM m}{R + R} = - \frac{GM m}{2 R}$

Work done $W = Δ U = U_{f} - U_{i}$

$W = - \frac{GM m}{2 R} - (- \frac{GM m}{R}) = \frac{GM m}{2 R}$

Using the relation $g = \frac{GM}{R ^{2}}$ , we get $GM = g R^{2}$

Substituting this in the expression for work done:

$W = \frac{g R ^{2} m}{2 R} = m g \frac{R}{2}$

Answer: $m g \frac{R}{2}$

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