If $V, R$ and $g$ denote respectively the escape velocity from the surface of the earth,the radius of the earth,and the acceleration due to gravity,then the correct equation is:

$A$ planet has twice the radius but the mean density is $\frac{1}{4}^{th}$ as compared to Earth. What is the ratio of the escape velocity from Earth to that from the planet?

$A$ spaceship is stationed on Mars. How much energy must be expended on the spaceship to launch it out of the solar system? Mass of the spaceship $= 1000 \; kg$,mass of the Sun $= 2 \times 10^{30} \; kg$,mass of Mars $= 6.4 \times 10^{23} \; kg$,radius of Mars $= 3395 \; km$,radius of the orbit of Mars $= 2.28 \times 10^{8} \; km$,$G = 6.67 \times 10^{-11} \; N m^{2} kg^{-2}$.

Escape velocity at the surface of the Earth is $11.2 \, km/s$. If the radius of a planet is double that of the Earth but its mean density is the same as that of the Earth,then the escape velocity will be ........ $km/s$.

$A$ body is projected vertically upwards from the surface of the earth with a velocity equal to half the escape velocity. If $R$ is the radius of the earth,the maximum height attained by the body from the surface of the earth is

If a body of mass $1\text{ kg}$ falls on the earth from infinity, it attains velocity $(v)$ and kinetic energy $(k)$ on reaching the surface of earth. The values of $v$ and $k$ respectively are . . . . . . . (Take radius of earth to be $6400\text{ km}$ and $g = 9.8\text{ m/s}^2$)