Physics - Gravitation Question with Solution | TestHub

The acceleration due to gravity at a height $h$ above the Earth's surface is given by $g_h=g{\left(\frac{R}{R+h}\right)}^2$. The acceleration due to gravity at a depth $d$ below the Earth's surface is given by $g_d=g\left(1-\frac{d}{R}\right)$. Given $g_h=g_d$ and $h=R/2$:$$g{\left(\frac{R}{R+R/2}\right)}^2=g\left(1-\frac{d}{R}\right)$$ $${\left(\frac{R}{3R/2}\right)}^2=1-\frac{d}{R}$$ $${\left(\frac{2}{3}\right)}^2=1-\frac{d}{R}$$ $$\frac{4}{9}=1-\frac{d}{R}$$ $$\frac{d}{R}=1-\frac{4}{9}=\frac{5}{9}$$ $$d=\frac{5R}{9}$$