Answer to Question #163639 in Mechanics | Relativity for Danfulde

Question

The base of a mountain is at sea level where the gravitational field strength is 9.810N/kg. The value of the gravitational field strength at the top of the mountain is 9.790N/kg. Calculate the height of the mountain above the sea level.

Answer 1

By the definition of the gravitational field strength, we have:

$$g=\dfrac{GM}{R^2}.$$

Then, we can write:

$$\dfrac{g_{sea}}{g_{top}}=\dfrac{\dfrac{GM}{R^2}}{\dfrac{GM}{(R+h)^2}}=\dfrac{(R+h)^2}{R^2},$$ $$\sqrt{\dfrac{g_{sea}}{g_{top}}}=\dfrac{R+h}{R},$$ $$h=R(\sqrt{\dfrac{g_{sea}}{g_{top}}}-1),$$ $$h=6.38\cdot10^6\ m\cdot(\sqrt{\dfrac{9.81\ \dfrac{N}{kg}}{9.79\ \dfrac{N}{kg}}}-1)=6513\ m.$$