Question

the acceleration due to gravity, at a depth d below the surface of earth,equal gravity at depth.obtained the formula for the ratio (gd /ge) where ge is the acceleration due to gravity on the surface of the earth ​

Answer 1

Hey buddy,

● Answer -
gd/ge = 1 - d/R


● Explanation -
[Refer to image for figure.]

Let gd be acceleration due gravity at depth d from surface.
gd = (4/3) πG(R-d) / ρ

Also ge be acceleration due to gravity at earth surface -
ge = (4/3) πGR / ρ

Taking ratio of gd/ge -
gd/ge = [(4/3)πG(R-d)/ρ] / [(4/3)πG(R-d)/ρ]
gd/ge = (R-d)/R
gd/ge = 1 - d/R

Hope thiz helped...