The ratio of the radii of planets $A$ and $B$ is ${k_1}$ and the ratio of acceleration due to gravity on them is ${k_2}$. The ratio of escape velocities from them will be

$A$ body is projected vertically upwards from the surface of the earth with a speed of $k{v_e}$,where $k < 1$ and ${v_e}$ is the escape velocity of the earth. What is the maximum height from the center of the earth that the body will reach? (Given: $R$ is the radius of the earth)

The condition for a uniform spherical mass $m$ of radius $r$ to be a black hole is [$G=$ gravitational constant and $c=$ speed of light]

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

If $V, R$ and $g$ denote respectively the escape velocity from the surface of the earth,the radius of the earth,and the acceleration due to gravity,then the correct equation is:

How much energy is necessary for a body of $500 \, kg$ to escape from the Earth? $[g = 9.8 \, m/s^2$,radius of Earth $R = 6.4 \times 10^6 \, m]$