$A$ particle is kept at rest at a distance $R$ from the surface of the Earth (of radius $R$). The minimum speed with which it should be projected so that it does not return is

On which two factors does the escape velocity of an object projected from the Earth $NOT$ depend?

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

State two factors that determine whether a planet will have an atmosphere or not.

Gravitational acceleration on the surface of a planet is $\frac{\sqrt{6}}{11}g$,where $g$ is the gravitational acceleration on the surface of the earth. The average mass density of the planet is $\frac{2}{3}$ times that of the earth. If the escape speed on the surface of the earth is taken to be $11 \ km/s$,the escape speed on the surface of the planet in $km/s$ will be:

$A$ 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