Question

What is the fractional decrease in the value of free fall acceleration g for a particle when it is lifted from the surface to an elevation h? (h $≪$ R)

Moderate

Solution

We know that, $g = \frac{G M}{R^{2}} \Rightarrow \frac{d g}{d R} = \frac{- 2 G M}{R^{3}}$
$\Rightarrow \frac{d g}{d R} = \frac{- 2 G M}{R^{2}} . \frac{1}{R}$
$\Rightarrow \frac{d g}{g} = - 2 (\frac{h}{R}) (∵ d R = h)$

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