Question

At what height above the earth's surface the value of $g$ is same as that at a depth of $100km$? (Take $g_h=g_d$)

Answer 1

Let height be 'h'

We know that the variation of 'g' with height

$g_h=g_0(1-\frac{2h}{R}).........\left(i\right)$

And the variation of 'g' with depth

$g_d=g_0(1-\frac{d}{R}).........\left(ii\right)$

According to the question,

$g_h=g_d$

So,

$g_0(1-\frac{2h}{R})=g_0(1-\frac{d}{R})$

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

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

$h=\frac{100}{2}$

$h=50km$