Two planets $A$ and $B$ have densities $\varrho_1$ and $\varrho_2$ and have radii $r_1$ and $r_2$ respectively. The ratio of acceleration due to gravity on $A$ to that of $B$ is:

Acceleration due to gravity is $g$ on the surface of the earth. The value of acceleration due to gravity at a height of $32 \, km$ above the earth's surface is ........ $g$. (Radius of the earth $= 6400 \, km$)

Two planets have radii $R_1$ and $R_2$ and densities $\rho_1$ and $\rho_2$ respectively. Find the ratio of the acceleration due to gravity on these planets.

Imagine Earth to be a solid sphere of mass $M$ and radius $R$. If the value of acceleration due to gravity at a depth $d$ below Earth's surface is the same as its value at a height $h$ above its surface and equal to $\frac{g}{4}$ (where $g$ is the value of acceleration due to gravity on the surface of Earth),the ratio of $\frac{h}{d}$ will be

$A$ body of weight $W$ is projected vertically upwards from the Earth's surface to reach a height above the Earth which is equal to nine times the radius of the Earth. The weight of the body at that height will be

$A$ hole is drilled through the Earth along a diameter and a stone is dropped into it. When the stone reaches the center of the Earth,which of the following quantities remains constant?