The radius and mean density of a planet are four times that of the Earth. The ratio of the escape velocity on the Earth to the escape velocity on the planet is:

$A$ particle falls towards the Earth from infinity. Its velocity on reaching the Earth would be:

$A$ body of mass $m$ is projected with velocity $\lambda v_{e}$ in a vertically upward direction from the surface of the earth into space. It is given that $v_{e}$ is the escape velocity and $\lambda < 1$. If air resistance is considered to be negligible,then the maximum height from the center of the earth,to which the body can go,will be: ($R$: radius of earth)

The ratio of accelerations due to gravity $g_{1}:g_{2}$ on the surfaces of two planets is $5:2$ and the ratio of their respective average densities $\rho_{1}:\rho_{2}$ is $2:1$. What is the ratio of respective escape velocities $v_{1}:v_{2}$ from the surface of the planets?

The escape speed of an object on the surface of the earth is $V$. If the object is thrown out with speed $4V$ from the surface of the earth,what will be the speed of the object far away from the earth?

$A$ body is projected from the earth's surface with a speed $\sqrt{5}$ times the escape speed $(V_{e})$. The speed of the body when it escapes from the gravitational influence of the earth is