If the radius and acceleration due to gravity both are doubled,the escape velocity of the Earth will become ......... $km/s$.

An object is thrown vertically upwards from the surface of the earth with a velocity $x$ times the escape velocity on the earth $(x < 1)$. The maximum height to which it rises from the center of the earth is (radius of earth is $R$):

$A$ body is projected vertically from the Earth's surface with a velocity equal to half the escape velocity. The maximum height reached by the body is ($R =$ radius of the Earth).

The escape velocity of a body from the Earth is about $11.2 \, km/s$. Assuming the mass and radius of the Earth to be about $81$ and $4$ times the mass and radius of the Moon,respectively,the escape velocity in $km/s$ from the surface of the Moon will be .......

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

$A$ rocket is fired vertically with a speed of $4 \ km/s$ from the Earth's surface. How far from the Earth does the rocket go before returning to the Earth (in $km$)? (Take radius of Earth $R = 6.4 \times 10^6 \ m$ and $g = 10 \ m/s^2$)