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Variation of g (Acceleration Due to Gravity)

A body is rel...

Question

A body is released at a distance far away from the surface of the earth. Calculate its speed when it is near the surface of earth. Given $g = 9.8$ m $s^{- 2}$ , radius of earth $R = 6.37 \times 10^{6}$ m.

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Solution

$\frac{G M m}{R} = \frac{1}{2} m v^{2} v = \sqrt{\frac{2 G M}{R}} = 11 k m / s$

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