Weight of a body is maximum at

The height at which the acceleration due to gravity becomes $\frac{g}{9}$ (where $g$ = the acceleration due to gravity on the surface of the earth) in terms of $R$,the radius of the earth,is

The radii of two planets $A$ and $B$ are $R$ and $4R$ and their densities are $\rho$ and $\rho/3$ respectively. The ratio of acceleration due to gravity at their surfaces $(g_A : g_B)$ will be

The depth $d$ at which the acceleration due to gravity becomes $\frac{g}{n}$ is (where $R$ is the radius of the Earth,$g$ is the acceleration due to gravity at the surface,and $n$ is an integer).

For a sphere of mass $M$ and radius $R$,if the gravitational forces at distances $r_1$ and $r_2$ from the center are $F_1$ and $F_2$ respectively,then:

If the acceleration due to gravity at the Earth is $g$,the mass of the Earth is $80$ times that of the Moon,and the radius of the Earth is $4$ times that of the Moon,then the value of the acceleration due to gravity at the surface of the Moon will be: