Physics - Gravitation Question with Solution | TestHub

The acceleration due to gravity at a depth $d$ is given by:

$g_d=g\left(1-\frac{d}{R}\right)$

The acceleration due to gravity at a height $h$ (where $h\ll R$) is given by:

$g_h=g\left(1-\frac{2h}{R}\right)$

Given that the acceleration due to gravity at height $h$ is equal to that at depth $d=90$ km:

$g_h=g_d$

$g\left(1-\frac{2h}{R}\right)=g\left(1-\frac{d}{R}\right)$

$\frac{2h}{R}=\frac{d}{R}$

$2h=d$

$h=\frac{d}{2}$

Substituting $d=90$ km:

$h=\frac{90}{2}=45$ km

Answer: $45$ km