The acceleration due to gravity at pole and equator can be related as

A satellite is revolving around the earth in a circular orbit with kinetic energy of $$1.69 \times 10^{10} \mathrm{~J}$$. The additional kinetic energy required for just escaping into the outer space 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