The ratio of the acceleration due to gravity on two planets $P_1$ and $P_2$ is $K_1$. The ratio of their respective radii is $K_2$. The ratio of their respective escape velocities is

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?

$A$ rocket is projected in the vertically upwards direction with a velocity $kv_e$,where $v_e$ is the escape velocity and $k < 1$. The distance from the centre of the Earth up to which the rocket will reach 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

If the escape velocity of a body of mass $1\,kg$ from the surface of the Earth is $11.2\,km/s$,then what is the escape velocity for a body of mass $10\,kg$?

$A$ projectile is projected with velocity $k{v_e}$ in the vertically upward direction from the ground into space. (${v_e}$ is the escape velocity and $k < 1$). If air resistance is considered to be negligible,then the maximum height from the center of the Earth to which it can go will be: ($R$ = radius of Earth)