Two planets $A$ and $B$ have the same material density. If the radius of $A$ is twice that of $B,$ then the ratio of the escape velocity $\frac{V_A}{V_B}$ is

Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$.
Assertion $A$: Earth has an atmosphere,whereas the Moon does not have any atmosphere.
Reason $R$: The escape velocity on the Moon is very small compared to that on the Earth.
In the light of the above statements,choose the correct answer from the options given below:

The escape velocity of an atmospheric particle which is $1000 \, km$ above the Earth's surface is .......... $km/s$ (radius of Earth is $6400 \, km$ and $g = 9.8 \, m/s^2$).

Find the kinetic energy required to project an object of mass $m$ from the surface of the Earth to infinity.

The escape velocity of a body on an imaginary planet,which has thrice the radius of the Earth and double the mass of the Earth,is (where $v_e$ is the escape velocity of Earth):

"The value of the escape velocity $v_e$ for a stationary object on the surface of a planet is directly proportional to the mass and radius of the planet." Is this statement correct? If not,correct it.