The escape velocity of a body on the surface of the earth is $11.2 \, km/s$. If the earth's mass increases to twice its present value and the radius of the earth becomes half,the escape velocity would become ......... $km/s$.

The escape velocity of a body from the surface of the earth is $11.2 \,km/s$. The escape velocity of a body from a planet having the same mean density as the earth but twice the radius of earth is: (in $\,km/s$)

The ratio of the orbital velocity of a body near the surface of a planet to the escape velocity of a body from the surface of the same planet is:

$A$ rocket has to be launched from the Earth in such a way that it never returns. If $E$ is the minimum energy delivered by the rocket launcher,what should be the minimum energy that the launcher should have if the same rocket is to be launched from the surface of the Moon? Assume that the density of the Earth and the Moon are equal and that the Earth's volume is $64$ times the volume of the Moon.

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

$A$ particle is projected vertically up with velocity $v = \sqrt{\frac{4 g R_e}{3}}$ from the Earth's surface. The velocity of the particle at a height equal to half of the maximum height reached by it is .........