Answer to Question #350297 in Physics for Geral

Question

If the gravitational field strength at the top of Mount Everest is 9.772 N/kg, approximately how tall (in

feet) is the mountain?

Answer 1

$$g(h)=G\frac{M}{(R+h)^2}=G\frac{M}{R^2}*\frac{R^2}{(R+h)^2}$$

$$g(h)=g(0)\frac{R^2}{(R+h)^2}$$

$$9.772=9.807*\left(\frac{6378}{6378+h}\right)^2$$

$$\frac{6378}{6378+h}=0.998$$

$$h=11.41\:\rm km=37 434\: ft$$