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 :

Options

A. d = 1 km
B. `d = 3/2 km`
C. `d = 2km`
D. `d = 1/2 km`

Answer

C

Explanation

The acceleration due to gravity at a height h is given as `g_h = g(1-2h//R_e)` where `R_e` is radius of earth.
The acceleration due to gravity at a depth d is given as
` g_d = g (1-d//R_e) "given " g_h = g_d `
` therefore g (1 - (2h)/(R_e)) = g (1 - (d)/(R_e))`
` therefore d = 2h = 2 xx 1 =2km" " (because h = 1 km)`