Question

at what height above the earth's surface the value of g is same as in a mine 80km deep

Answer 1

we know that for variation of g with height(h),
g' = g(1- 2h/R)
and for variation of g with depth(d)
g' = g(1- d/R)

According to the question,
g(1- 2h/R) = g(1- d/R)
⇒ 1- 2h/R = 1- d/R
⇒ 2h/R = d/R
⇒ 2h = d
⇒ 2h = 80 Km            
⇒ h = 40 Km (Ans.)

Answer 2

g(1- 2h/R) = g(1- d/R)

⇒ 1- 2h/R = 1- d/R

⇒ 2h/R = d/R

⇒ 2h = d

⇒ 2h = 80 Km    

h= 40km