Q134 / 160 · AP EAMCET 2021 (19 Aug Shift 2) · Physics

The distance through which one has to dig the earth from its surface so as to reach the point where the acceleration due to gravity is reduced by $40 %$ of that at the surface of the earth, is (radius of earth is $6400 km$ )

Solution

Acceleration due to gravity, $g_{d} = g (1 - \frac{d}{R})$

$\Rightarrow \frac{g_{d}}{g} = (1 - \frac{d}{R})$

$\Rightarrow 1 - \frac{40}{100} = (1 - \frac{d}{R})$

$\Rightarrow \frac{d}{R} = (\frac{40}{100})$

$\Rightarrow d = R (\frac{40}{100}) = 2560 km$

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