Find gravitational field at a distance of 2000 km from Jibe centre of earth. (Take, R_earth = 6400 km, r = 2000 km, M_earth = 6 X 1024 kg) [AIIMS 2019]

Given, radius of earth,  R_e = 6400 km = 6.4 $6.4 \times {10}^6 m$

Distance from centre of earth, r = 2000 km
Distance from the surface of earth,

$d=R_e-r=6400-2000$

$=4400 \mathrm{km}=44\times {10}^6 \mathrm{m}$

H g' be the gravitational field below the surface of earth at a depth d, then

$g^{\text{'}}=g\left(1-\frac{d}{R_e}\right)=9.8\left(1-\frac{44\times {10}^6}{6.4\times {10}^6}\right) \left(\because g=9.8{ \mathrm{ms}}^{-2}\right)$

$=9.8\times 0.3125=3.06{ \mathrm{ms}}^{-2}$.