Question

the accleration due to gravity at a depth d below the earth sutface equal gd obtain the formula from the ration gd\ge where ge is tje accleration due to gravity on surface of earth​

Answer 1

Gravity g = G M / R²

gravity above Earth's surface = g'  ,  at altitude h.

       g'/g = R² / (R +h)² = 1 - 2 h/R

gravity below Earth's surface = g"   at a depth d kind radius R".
     M" / M =  R"³ / R³
     g" / g = (R² / R"² ) * (R"³ / R³)    =  R" / R
               =  (R - d) / R = 1 - d/R

     g" / g'  =  (R - d) / (R - 2 h)

     if d = h = R/20  then:

     g " / g'   =  (19R /20) / (18R/20)  = 19/18

     g" = 19/18  * 9 m/sec²  = 76/9 = 9.5 m/sec²