First slide

Gravitaional potential energy

Question

A body of mass M is taken from the surface of the earth to a height equal to the radius fi of the earth. The change in gravitational potential energy is

Moderate

A

2 MgR
B

MgR
C

MgR /2
D

MgR/4

Solution

${ΔU}_{p} = {GMM}_{e} [\frac{1}{R} - \frac{1}{R + h}]$
$\begin{array}{l} = {GMM}_{e} [\frac{1}{R} + \frac{1}{2 R}] \\ = \frac{{GMM}_{e}}{2 R} = \frac{M}{2} (\frac{{GM}_{e}}{R^{2}}) R = \frac{MgR}{2} \end{array}$

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