Question

The acceleration due to gravity at a height(1/20)th the radius of the earth above the earths surface is 9m/sec sq. it's value at a point at an equal distance below the surface of the earth is

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 and 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

Answer 2

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 and 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