Find ratio of acceleration due to gravity `g` at depth `d` and at height `h` where `d=2h`

Options

A. `1:1`
B. `1:2`
C. `2:1`
D. `1:4`

Answer

A

Explanation

If `g'` is the acceleration due to gravity at a point, a a height `h` above the surface of earth and `g` be acceleration due to gravity on earth's surface, then
`g'=g(1-(2h)/R)`…………..i
`g"=g(1-d/R)`…………ii
But, `d=h` [given]
`:.g"=g(1-(2h)/R)`.............iii
`:.(g")/(g')=(g(1-(2h)/R))/(g(1-(2h)/R))=1`
`:.g":g'=1:`