$A$ body is projected vertically upwards from the surface of the Earth with a velocity equal to one-third of the escape velocity. The maximum height attained by the body will be $...... \ km$. (Take radius of Earth $R = 6400 \ km$ and $g = 10 \ m/s^2$)

Is it necessary to provide an initial speed of $11.2 \, km/s$ to a rocket launched from Earth?

$A$ particle is projected vertically up with velocity $v = \sqrt{\frac{4 g R_e}{3}}$ from the Earth's surface. The velocity of the particle at a height equal to half of the maximum height reached by it is .........

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

Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$.
Assertion $A$: The kinetic energy needed to project a body of mass $m$ from the Earth's surface to infinity is $\frac{1}{2} mgR$,where $R$ is the radius of the Earth.
Reason $R$: The maximum potential energy of a body is zero when it is projected to infinity from the Earth's surface.
In the light of the above statements,choose the correct answer from the options given below.

$A$ body is projected vertically upwards from the surface of a planet of radius $R$ with a velocity equal to half the escape velocity for that planet. The maximum height attained by the body is