A planet has double the mass of the earth and double the radius. The gravitational potential at the surface of the Earth is $$\mathrm{V}$$ and the magnitude of the gravitational field strength is $$\mathrm{g}$$. The gravitational potential and gravitational field strength on the surface of the planet are
| Potential | Field | |
|---|---|---|
| A | V | $$\frac{g}{4}$$ |
| B | 2V | $$\frac{g}{2}$$ |
| C | V | $$\frac{g}{2}$$ |
| D | 2V | $$\frac{g}{4}$$ |
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