$A$ rocket is launched with velocity $10 \ km/s$. If the radius of the Earth is $R$,then the maximum height attained by it will be: (in $R$)

$A$ spaceship moves from the Earth to the Moon and back. The greatest energy required for the spaceship is to overcome the difficulty in:

An object is thrown directly away from the surface of the earth with an initial speed $v$. The object reaches up to a height of $\frac{4}{5} R_E$ from the earth's surface,where $R_E$ is the radius of the earth. If the escape velocity of the object is $v_E$,then the value of $\frac{v}{v_E}$ is:

If the radius of a planet is four times that of Earth and the value of $g$ is the same for both,the escape velocity on the planet will be ......... $km/s$.

The escape velocity for the earth is $v_e$. The escape velocity for a planet whose radius is four times and density is nine times that of the earth,is (in $,v_e$)

Two stars of masses $3\times10^{31} \ kg$ each,and at distance $2\times10^{11} \ m$ rotate in a plane about their common centre of mass $O$. $A$ meteorite passes through $O$ moving perpendicular to the star's rotation plane. In order to escape from the gravitational field of this double star,the minimum speed that the meteorite should have at $O$ is: (Take Gravitational constant $G = 6.67\times10^{-11} \ Nm^2 \ kg^{-2}$)