Earth binds the atmosphere because of

$A$ 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 $R$)

The escape velocity for a body of mass $1\, kg$ from the earth's surface is $11.2\, km/s$. The escape velocity for a body of mass $100\, kg$ would be:

Escape velocity at the surface of the Earth is $11.2 \, km/s$. If the radius of a planet is double that of the Earth but its mean density is the same as that of the Earth,then the escape velocity will be ........ $km/s$.

Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$.
Assertion $A :$ The escape velocities of planet $A$ and $B$ are same. But $A$ and $B$ are of unequal mass.
Reason $R :$ The product of their mass and radius must be same,$M_{1}R_{1} = M_{2}R_{2}$.
In the light of the above statements,choose the most appropriate answer from the options given below.

$A$ body is projected vertically upwards from the surface of the earth with a velocity equal to half the escape velocity. If $R$ is the radius of the earth,the maximum height attained by the body from the surface of the earth is