$A$ ball $A$ of mass $m$ falls to the surface of the earth from infinity. Another ball $B$ of mass $2m$ falls to the earth from a height equal to six times the radius of the earth. The ratio of the velocities of $A$ and $B$ on reaching the earth is:

$A$ rocket is launched straight up from the surface of the earth. When its altitude is $\frac{1}{3}$ of the radius of the earth,its fuel runs out and therefore it coasts. If the rocket has to escape from the gravitational pull of the earth,the minimum velocity with which it should coast is (Escape velocity on the surface of the earth is $11.2 \ km/s$.) (in $km/s$)

The mass of a planet is half that of the Earth and the radius of the planet is one-fourth that of the Earth. If we plan to send an artificial satellite from the planet,the escape velocity will be (escape velocity on Earth $v_e = 11 \ km \ s^{-1}$): (in $km \ s^{-1}$)

State two factors that determine whether a planet will have an atmosphere or not.

$A$ spaceship moves from the Earth to the Moon and back. The greatest energy required for the spaceship is to overcome the difficulty in:

$A$ particle of mass $m$ is kept at rest at a height $3R$ from the surface of the Earth,where $R$ is the radius of the Earth and $M$ is the mass of the Earth. The minimum speed with which it should be projected upward so that it does not return back is ($g$ = acceleration due to gravity on the Earth's surface).