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:

By approximately how many meters is the radius of the Earth at the equator greater than the radius of the Earth at the poles (in $,000 \ m$)?

$A$ research satellite of mass $200 \,kg$ circles the earth in an orbit of average radius $3R/2$,where $R$ is the radius of the earth. Assuming the gravitational pull on a mass of $1 \,kg$ on the earth's surface to be $10 \,N$,the pull on the satellite will be ........ $N$.

If the density of a small planet is the same as that of the Earth,while the radius of the planet is $0.2$ times that of the Earth,the gravitational acceleration on the surface of that planet is .......... $g$.

The value of $g$ at a particular point is $9.8\,m/s^2$. Suppose the Earth suddenly shrinks uniformly to half its present size without losing any mass. The value of $g$ at the same point (assuming that the distance of the point from the centre of the Earth does not shrink) will now be ......... $m/s^2$.

The height at which the weight of a body becomes $\left(\frac{1}{9}\right)^{\text{th}}$ of its weight on the surface of the Earth is $(R = \text{radius of Earth})$: (in $R$)