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 ......... $km/s$.

$A$ body is projected from the earth's surface with a speed $\sqrt{5}$ times the escape speed $(V_{e})$. The speed of the body when it escapes from the gravitational influence of the earth is

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 masses and radii of the Earth and Moon are $M_1, R_1$ and $M_2, R_2$ respectively. Their centres are at a distance $d$ apart. The minimum speed with which a body of mass $m$ should be projected from a distance $2d/3$ from the centre of $M_1$ so as to escape to infinity is:

The escape velocity of a projectile from the earth is approximately .......... $km/sec$.

For the moon to cease to remain the earth's satellite,its orbital velocity has to increase by a factor of