The acceleration due to gravity on a planet is the same as that on Earth,and its radius is four times that of Earth. What will be the value of the escape velocity on that planet if it is $v_e$ on Earth?

The ratio of the acceleration due to gravity on two planets $P_1$ and $P_2$ is $K_1$. The ratio of their respective radii is $K_2$. The ratio of their respective escape velocities 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 ratio of the orbital velocity of a body near the surface of a planet to the escape velocity of a body from the surface of the same planet is:

Masses and radii of Earth and Moon are $M_1, M_2$ and $R_1, R_2$ respectively. The distance between their centers is $d$. The minimum velocity given to a mass $m$ from the midpoint of the line joining their centers so that it escapes the gravitational field of both is:

The masses and radii of the Earth and the Moon are $M_1, R_1$ and $M_2, R_2$ respectively. Their centres are at a distance $d$ apart. The minimum speed with which a particle of mass $m$ should be projected from a point midway between the two centres so as to escape to infinity is