Let `g_(h)` and `g_(d)` the acceleration due to gravity at height h above the earth s surface and at depth d below the earth surface respecitively if `g_(h) = g_(d)` then the releation between h and d is

Options

A. `d=h`
B. `d=(h)/(2)`
C. `d=(h)/(4)`
D. `d=2h`

Answer

D

Explanation

Accelearation due to gravity at a height h above the earth 's surface
`g_(h)=g(1-(2h)/(R ))`
Acceleration due to gravity at a depth d below the earth 's suface
`g_(d)=g(1-(d)/(R ))`
as `g_(h)=g_(d)`
or `1-(2h)/(R )=1-(d)/(h)`
`rarr (2h)/(R )=(d)/(R )`
`rarr d=2h`