The acceleration due to gravity at a height 1 km above the earth is the same as at a depth d below the surface of earth. Then :

Question

The acceleration due to gravity at a height 1 km above the earth is the same as at a depth d below the surface of earth. Then : (A) d = 1 km  (B) d = (3/2) km  (C) d = 2 k m  (D)  d = (1/2) km

Tardigrade Admin · Accepted Answer

Above earth surface g'=g(1-(2 h/Re)) Δ g'=g (2 h/Re)...(1) From (1) (2) d=2 h d=2 × 1 km Below earth surface g'=g(1-(d/Re)) Δ g=g (d/Re)...(2)

Q. The acceleration due to gravity at a height $1 km$ above the earth is the same as at a depth $d$ below the surface of earth. Then :

$d = 1 km$

$d = \frac{3}{2} km$

$d = 2 km$

$d = \frac{1}{2} km$

Above earth surface
$g^{'} = g (1 - \frac{2 h}{R _{e}})$
$Δ g^{'} = g \frac{2 h}{R _{e}}$ ...(1)
From (1) & (2)
$d = 2 h$
$d = 2 \times 1 km$
Below earth surface
$g^{'} = g (1 - \frac{d}{R _{e}})$
$Δ g = g \frac{d}{R _{e}}$ ...(2)

Q. The acceleration due to gravity at a height 1km above the earth is the same as at a depth d below the surface of earth. Then :

d=1km

d=23​km

d=2km

d=21​km