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

The ratio of the radii of planets $A$ and $B$ is ${k_1}$ and the ratio of acceleration due to gravity on them is ${k_2}$. The ratio of escape velocities from them will be

On which two factors does the escape velocity of an object projected from the Earth $NOT$ depend?

Given the mass of the moon is $1/81$ of the mass of the earth and its radius is $1/4$ of the earth's radius. If the escape velocity on the earth's surface is $11.2 \, km/s$,the value of the escape velocity on the surface of the moon is ......... $km/s$.

The radius of the planet is double that of the earth,but their average densities are same. $V_{p}$ and $V_E$ are the escape velocities of planet and earth respectively. If $\frac{V_p}{V_E}=x$,the value of '$x$' is

Earth has mass $M_1$ and radius $R_1$,and the moon has mass $M_2$ and radius $R_2$. The distance between their centers is $r$. $A$ body of mass $M$ is placed on the line joining them at a distance $r/3$ from the center of the Earth. To project the mass $M$ to escape to infinity,the minimum speed required is: