$A$ body is projected vertically from earth's surface with $\left(\frac{1}{3}\right)^{\text{rd}}$ of escape velocity. The maximum height reached by the body is ($R=$ radius of earth).

The escape speed of an object on the surface of the earth is $V$. If the object is thrown out with speed $4V$ from the surface of the earth,what will be the speed of the object far away from the earth?

$A$ ball $A$ of mass $m$ falls to the surface of the earth from infinity. Another ball $B$ of mass $2m$ falls to the earth from a height equal to six times the radius of the earth. The ratio of the velocities of $A$ and $B$ on reaching the earth is:

The escape velocity for the Earth is $11 \ km/s$. The escape velocity for a planet having twice the radius and the same density as the Earth is .......... $km/s$.

Masses and radii of Earth and Moon are $M_1, M_2$ and $R_1, R_2$ respectively. The distance between their centers is $d$. The minimum velocity given to a mass $m$ from the midpoint of the line joining their centers so that it escapes the gravitational field of both is:

The escape velocity of a body from a planet of mass $M$ and radius $R$ is $14 \,km \,s^{-1}$. The escape velocity of the body from another planet having same mass and diameter $8R$ (in $km \,s^{-1}$) is