Energy required for moving a body of mass $$\mathrm{m}$$ from a circular orbit of radius 3R to a higher orbit of radius 4R around the earth is.

If $$\mathrm{A}$$ is the areal velocity of a planet of mass $$\mathrm{M}$$, then its angular momentum is

If the earth has a mass nine times and radius four times that of planet X, the ratio of the maximum speed required by a rocket to pull out of the gravitational force of planet $$\mathrm{X}$$ to that of the earth is

Starting from the centre of the earth having radius $$R$$, the variation of $$g$$ (acceleration due to gravity) is shown by