Question

Value of $g$ on the surface of earth is $9.8m/s^2$. Value of $g$ on the surface of earth is $9.8m/s^2$. At height $h=R$ from the surface the value of $g$ is $\frac{g}{x}$. Find $x$.

Answer 1

Surface gravity, $g=\frac{GM}{R^2}$ and gravity at height h from earth's surface is $g^{\prime }=\frac{GM}{(R+h{)}^2}$

so, $\frac{g^{\prime }}{g}=\frac{R^2}{(R+h{)}^2}$

At $h=R$, $\frac{g^{\prime }}{g}=\frac{R^2}{(R+R{)}^2}=1/4$

so $g^{\prime }=g/4$