1. Given data

   • Height of point $P$ above the earth's surface is equal to the diameter of earth.
   • Let radius of earth be $R$.
   • Then diameter of earth $= 2R$.
   • So height of point $P$ above the surface is $h = 2R$

2. Distance of point $P$ from the center of earth The point is above the surface, so its distance from the center is $r = R + h = R + 2R = 3R$

3. Formula for acceleration due to gravity at height $h$ At a distance $r$ from the center of earth, g' = rac{GM}{r^2} and at the surface, g = rac{GM}{R^2}

   Therefore, $\frac{g'}{g} = \frac{GM/r^2}{GM/R^2} = \frac{R^2}{r^2}$

4. Substitute $r = 3R$ $\frac{g'}{g} = \frac{R^2}{(3R)^2} = \frac{1}{9}$

   Hence, $g' = \frac{g}{9}$

5. Option check

   • A: $g/2$ ❌
   • B: $g/4$ ❌
   • C: $g/3$ ❌
   • D: $g/9$ ✅

Therefore, the correct answer is Option D.