The escape velocity of a body from the Earth is about $11.2 \, km/s$. Assuming the mass and radius of the Earth to be about $81$ and $4$ times the mass and radius of the Moon,respectively,the escape velocity in $km/s$ from the surface of the Moon will be .......

The potential energy of a satellite is $-8 \times 10^9 \ J$. What is its binding energy (escape energy)?

The escape velocity for the earth is $v_e$. The escape velocity for a planet whose radius is four times and density is nine times that of the earth,is (in $,v_e$)

$A$ small asteroid is orbiting around the sun in a circular orbit of radius $r_0$ with speed $v_0$. $A$ rocket is launched from the asteroid with speed $v = \alpha v_0$,where $v$ is the speed relative to the sun. The highest value of $\alpha$ for which the rocket will remain bound to the solar system is (ignoring gravity due to the asteroid and effects of other planets).

$A$ body is projected vertically from the surface of the earth of radius $R$ with a velocity equal to half of the escape velocity. The maximum height reached by the body is

The escape velocity of a sphere of mass $m$ is given by ($G =$ Universal gravitational constant; $M_e =$ Mass of the earth and $R_e =$ Radius of the earth).