Gravitaional potential energy

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Question

The ratio of work done in taking a body from the surface of earth (Radius = R) to a height R above the surface of earth to the work done in placing the object in a circular orbit at that height is ____

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Solution

$\begin{array}{l} W_{1} = (- \frac{GMm}{2 R}) - (- \frac{GMm}{R}) = \frac{GMm}{2 R} \\ W_{2} = (- \frac{GMm}{4 R}) - (- \frac{GMm}{R}) = \frac{3}{4} \frac{GMm}{R} \\ ∴ W_{1} : W_{2} = 4 : 3 \end{array}$

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