The ratio of the radius of the Earth to that of the Moon is $10$. The ratio of acceleration due to gravity on the Earth and on the Moon is $6$. The ratio of the escape velocity from the Earth's surface to that from the Moon is

Earth binds the atmosphere because of

If $g$ is the acceleration due to gravity at the earth's surface and $r$ is the radius of the earth,the escape velocity for a body to escape out of the earth's gravitational field is

Consider a spherical planet which is rotating about its axis such that the speed of a point on its equator is $v$ and the effective acceleration due to gravity on the equator is $\frac{1}{3}$ of its value at the poles. What is the escape velocity for a particle at the pole of this planet?

Gas escapes from the surface of a planet because it acquires an escape velocity. The escape velocity will depend on which of the following factors :
$I.$ Mass of the planet
$II.$ Mass of the particle escaping
$III.$ Temperature of the planet
$IV.$ Radius of the planet
Select the correct answer from the codes given below :

If the radius of a planet is $R$ and its density is $\rho$,the escape velocity from its surface will be