# At what height above earth 's surface, value of g is same as in a mine 100 km deep?

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g = 0 ( 1- ) - (1)

g = 0 ( 1- ) - (2)

g = 0 ( 1- ) - (1) ≡ g = 0 ( 1- ) - (2)

⇒ =

⇒ h = = = 50 km

⇒ 50 km

variation of g with height=

g=g0(1-2h/r) -----(1)

variation in g with depth=

g=g0(1-d/r)---------(2)

g0(1-2h/r)=g0(1-d/r)

2h/r=d/r

h=d/2

=100/2=50km.