$A$ particle of mass $m_0$ is projected from the midpoint of the line joining two fixed particles,each of mass $m$. If the separation between the fixed particles is $l$,the minimum velocity of projection of the particle so as to escape is equal to:

$A$ rocket is launched straight up from the surface of the earth. When its altitude is $\frac{1}{3}$ of the radius of the earth,its fuel runs out and therefore it coasts. If the rocket has to escape from the gravitational pull of the earth,the minimum velocity with which it should coast is (Escape velocity on the surface of the earth is $11.2 \ km/s$.) (in $km/s$)

Why is there no atmosphere on the Moon? Explain it in terms of escape velocity.

Explain escape energy and provide its definition. Also, explain escape speed.

The mass of the Earth is $81$ times that of the Moon and the radius of the Earth is $3.5$ times that of the Moon. The ratio of the escape velocity on the surface of the Earth to that on the surface of the Moon will be:

$A$ 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: