The kinetic energy needed to project a body of mass $m$ from the earth's surface (radius $R$) to infinity is

$A$ rocket is launched with velocity $10 \ km/s$. If the radius of the Earth is $R$,then the maximum height attained by it will be: (in $R$)

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 :

The magnitude of potential energy per unit mass of an object at the surface of the Earth is $E$. Then,the escape velocity of the object is ..........

$A$ particle of mass $m$ is projected with a velocity $v = k V_{e}$ $(k < 1)$ from the surface of the earth. $(V_{e} = \text{escape velocity})$. The maximum height above the surface reached by the particle is:

$A$ satellite is moving with a constant speed '$V$' in a circular orbit about the Earth. An object of mass '$m$' is ejected from the satellite such that it just escapes from the gravitational pull of the Earth. At the time of its ejection,the kinetic energy of the object is