Two planets $A$ and $B$ have the same material density. If the radius of $A$ is twice that of $B,$ then the ratio of the escape velocity $\frac{V_A}{V_B}$ is

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

$A$ rocket is launched straight up from the surface of the earth. When its altitude is one-fourth of the radius of the earth,its fuel runs out and it coasts. What is the minimum velocity the rocket must have when it starts to coast if it is to escape from the gravitational pull of the earth? (Escape velocity on the surface of the earth is $11.2 \ km/s$)

$A$ certain object is projected vertically from the surface of the earth of radius $R$ with a velocity equal to half the escape velocity. The maximum height attained by the object will be

If $v_e$ is escape velocity and $v_0$ is orbital velocity of a satellite for an orbit close to the earth's surface,then these are related by:

The ratio of accelerations due to gravity $g_{1}:g_{2}$ on the surfaces of two planets is $5:2$ and the ratio of their respective average densities $\rho_{1}:\rho_{2}$ is $2:1$. What is the ratio of respective escape velocities $v_{1}:v_{2}$ from the surface of the planets?