At what depth below surface of the earth, the acceleration due to gravity will be half its value of that at 1600   km above the surface of the earth?

Question

At what depth below surface of the earth, the acceleration due to gravity will be half its value of that at 1600 &#160; km above the surface of the earth?

Aicharya · Accepted Answer

Acceleration due to gravity at a height, $g_{h} = g (1 - \frac{2 h}{R})$

$\Rightarrow g_{h} = g (1 - \frac{2 \times 1600 \times 10^{3}}{6400 \times 10^{3}})$

$\Rightarrow g_{h} = g (1 - 0.5)$

$\Rightarrow g_{h} = 5 m s^{- 2}$

Given, $2.5 = 10 (1 - \frac{d}{R})$

$\Rightarrow \frac{1}{4} = (1 - \frac{h}{R})$

$\Rightarrow \frac{3}{4} = (\frac{d}{R})$

$\Rightarrow d = \frac{3}{4} \times 6400 \times 10^{3}$

$\Rightarrow h = 4.8 \times 10^{6} m$

At what depth below surface of the earth, the acceleration due to gravity will be half its value of that at…

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