An artificial satellite moving in a circular orbit around the earth has a total (kinetic + potential) energy ${E_0}$. Its potential energy is

If $g$ is the acceleration due to gravity on the earth’s surface, the gain in the potential energy of object of mass $m$ raised from the surface of the earth to a height equal to the radius $R$ of the earth is

Two identical satellites $A$ and $B$ are circulating round the earth at the height of $R$ and $2R$ respectively, (where $R$ is radius of the earth). The ratio of kinetic energy of $A$ to that of $B$ is

If g is the acceleration due to gravity at the earth's surface and $r$ is the radius of the earth, the escape velocity for the body to escape out of earth's gravitational field is

The escape speed of a projectile on the earth's surface is $11.2\; km s ^{-1} .$ A body is projected out with thrice this speed. What is the speed (in $km/s$) of the body far away from the earth? Ignore the presence of the sun and other planets.