The ratio of the radii of two planets is $r$ and the ratio of accelerations due to gravity on the planets is $x$. Then the ratio of the escape velocities from the planets is

$A$ 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)

$A$ body is projected up with a velocity equal to $\frac{3}{4}$ of the escape velocity from the surface of the earth. The height it reaches is (Radius of the earth $= R$)

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

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

The velocity with which a projectile must be fired so that it escapes Earth's gravitation does not depend on