Question
At what height above the earth’s surface does the acceleration due to gravity fall to $1\%$ of its value at the earth’s surface ?
✓
Answer
Given $:$ $g_{h}=1 \% g_{s}=0.01 g_{s}$
Using $g_{h}=g_{s}\left(\frac{R}{R+h}\right)^{2}$
Or $\quad 0.01 g_{s}=g_{s}\left(\frac{R}{R+h}\right)^{2}$
or $\quad 0.1=\frac{R}{R+h}$
or $\quad 0.1 R+0.1 h=R$
$\Longrightarrow h=9 R$
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