Q135 / 160 · AP EAMCET 2021 (20 Aug Shift 2) · Physics

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?

Solution

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

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

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

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

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

Hence, the correct answer is option: 'A'.