There are two planets. The ratio of the radii of the two planets is $K$,and the ratio of the acceleration due to gravity of both planets is $g$. What will be the ratio of their escape velocities?

The escape velocity for a planet whose mass is six times the mass of Earth and whose radius is twice the radius of Earth will be (where $V_{e}$ is the escape velocity from the Earth).

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

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

$Assertion$: The escape speed does not depend on the direction in which the projectile is fired.
$Reason$: Attaining the escape speed is easier if a projectile is fired in the direction the launch site is moving as the Earth rotates about its axis.

$A$ bullet is fired vertically upwards with velocity $v$ from the surface of a spherical planet. When it reaches its maximum height,its acceleration due to the planet's gravity is $1/4$ of its value at the surface of the planet. If the escape velocity from the planet is $v_{esc} = v \sqrt{N}$,then the value of $N$ is (ignore energy loss due to atmosphere).