$A$ body is projected vertically upward 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 is:

Earth binds the atmosphere because of

An object is thrown vertically upwards from the surface of the earth with a velocity $x$ times the escape velocity on the earth $(x < 1)$. The maximum height to which it rises from the center of the earth is (radius of earth is $R$):

For a planet having mass equal to the mass of the Earth but a radius that is one-fourth of the radius of the Earth,the escape velocity for this planet will be (in $km/s$): (in $km/s$)

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

The radius of a planet is twice the radius of the Earth. Both have almost equal average mass densities. If $V_P$ and $V_E$ are the escape velocities of the planet and the Earth respectively,then: