If the escape velocity on Earth is $11.2 \text{ km/s}$, what is its value for a planet having double the radius and $8$ times the mass of Earth (in $\text{ km/s}$)?

$A$ body of mass $m$ is projected with velocity $\lambda v_{e}$ in a vertically upward direction from the surface of the earth into space. It is given that $v_{e}$ is the escape velocity and $\lambda < 1$. If air resistance is considered to be negligible,then the maximum height from the center of the earth,to which the body can go,will be: ($R$: radius of earth)

The escape velocity for a body projected vertically upwards from the surface of earth is $11.2 \ km/s$. If the body is projected at an angle of $45^o$ with the vertical,the escape velocity will be ......... $km/s$.

The mass of a spaceship is $1000 \ kg$. It is to be launched from the earth's surface out into free space. The value of $g$ and $R$ (radius of earth) are $10 \ m/s^2$ and $6400 \ km$ respectively. The required energy for this work will be

The ratio of the radius of a planet $A$ to that of planet $B$ is $r$. The ratio of acceleration due to gravity on the planets is $x$. The ratio of the escape velocities from the two planets is

Let the escape velocity of a body kept at the surface of a planet be $u$. If it is projected at a speed of $200 \%$ more than the escape speed,then its speed in interstellar space will be ...........